# Mind on Statistics. Chapter 15

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Mind on Statistics Chapter 15 Section A student survey was done to study the relationship between class standing (freshman, sophomore, junior, or senior) and major subject (English, Biology, French, Political Science, Undeclared, or Other). What are the degrees of freedom for the chi-square statistic? A. 4 B. 0 C. 15 D. 5. A student survey was done to study the relationship between where students live (dormitory, apartment, house, co-op, or parent s home) and how they usually get to campus (walking, bus, bicycle, car, or subway). What are the degrees of freedom for the chi-square statistic? A. 5 B. 16 C. 0 D A chi-square statistic was computed for a two-way table having 4 degrees of freedom. The value of the statistic was What is the p-value? A B C A chi-square statistic was computed for a two-way table having 0 degrees of freedom. The value of the statistic was What is the p-value? A B C A chi-square statistic was computed for a two-way table having 1 degree of freedom. The value of the statistic was What is the p-value? A B C

2 6. A chi-square statistic was computed for a two-way table having 1 degree of freedom. The value of the statistic was What is the p-value or p-value range? A. p-value < B < p-value < 0.05 C < p-value < A chi-square statistic was computed for a two-way table having 0 degrees of freedom. The value of the statistic was What is the p-value or p-value range? A. p-value = 0.05 B < p-value < C < p-value < A student survey was done to study the relationship between class standing (freshman, sophomore, junior, or senior) and favorite type of take-out food (pizza, Chinese food, burgers, sandwich, or other). The chi-square test statistic was 5. What is the p-value or p-value range? A < p-value < 0.05 B < p-value < 0.05 C < p-value < A student survey was done to study the relationship between gender and favorite television program watched on Sunday mornings (sports, news, or other). The chi-square test statistic was 10. What is the p-value or p-value range? A < p-value < 0.01 B < p-value < 0.05 C < p-value < Suppose that the chi-square statistic equals 10.9 for a two-way table with 4 rows and columns. In which range does the approximate p-value fall for this situation? A. Less than B. Between 0.01 and 0.05 C. Between 0.05 and 0.05 D. Between 0.10 and Which one of the following is NOT true about the table of expected counts for a chi-square test? A. The expected counts are computed assuming the null hypothesis is true. B. The expected counts are computed assuming the alternative hypothesis is true. C. The expected counts have the same row and column totals as the observed counts. D. The pattern of row percents is identical for all rows of expected counts. 1. A chi-square test involves a set of counts called expected counts. What are the expected counts? A. Hypothetical counts that would occur if the alternative hypothesis were true. B. Hypothetical counts that would occur if the null hypothesis were true. C. The actual counts that did occur in the observed data. D. The long-run counts that would be expected if the observed counts are representative. 318

3 13. Which of the following gives statistically significant results at the 0.05 level of significance? A. 7, df = 3 B. C. D. 0, df = 11 4, df = 15 10, df = Which of the following gives statistically significant results at the 0.01 level of significance? A. 9.1, df = B. C. D. 5.3, df = , df = , df = Which of the following gives statistically significant results? A. 10.3, df = 5, α = 0.05 B. C. D. 10.3, df = 4, α = , df = 7, α = , df = 3, α = Suppose that a two-way table displaying sample information about gender and opinion about the legalization of marijuana (yes or no) is examined using a chi-square test. The necessary conditions are met and the chi-square value is calculated to be 15. What conclusion can be made? A. Gender and opinion have a statistically significant relationship B. Gender and opinion do not have a statistically significant relationship C. It is impossible to make a conclusion because we don t know the sample size. D. It is impossible to make a conclusion because we don t know the degrees of freedom. 17. Which of the following relationships could be analyzed using a chi-square test? A. The relationship between height (inches) and weight (pounds). B. The relationship between satisfaction with K-1 schools (satisfied or not) and political party affiliation. C. The relationship between gender and amount willing to spend on a stereo system (in dollars). D. The relationship between opinion on gun control and income earned last year (in thousands of dollars). 18. For which of the following tests is the null hypothesis not of the form parameter = null value? A. A test for the difference in two proportions. B. A test for the mean of paired differences. C. A test for the difference in means for independent samples. D. A chi-square test of independence. 319

4 Questions 19 to 3: In the General Social Survey, respondents were asked what they thought was most important to get ahead: hard work, lucky breaks, or both. Minitab output for 106 respondents, by gender, is shown below: Expected counts are printed below observed counts Male Female Total Hard work Lucky breaks Both Total Chi-Sq = = P-Value = What is the null hypothesis for this situation? A. There is a relationship between gender and opinion on what is important to get ahead in the sample. B. There is no relationship between gender and opinion on what is important to get ahead in the sample. C. There is a relationship between gender and opinion on what is important to get ahead in the population. D. There is no relationship between gender and opinion on what is important to get ahead in the population. 0. What is the alternative hypothesis for this situation? A. There is a relationship between gender and opinion on what is important to get ahead in the sample. B. There is no relationship between gender and opinion on what is important to get ahead in the sample. C. There is a relationship between gender and opinion on what is important to get ahead in the population. D. There is no relationship between gender and opinion on what is important to get ahead in the population. 1. What is the value of the test statistic? A. 443 B. 583 C What are the degrees of freedom for the test statistic? A. B. 3 C At a significance level of 0.05, what is the conclusion? A. Reject the null hypothesis and conclude there is no relationship between the variables. B. Reject the null hypothesis and conclude there is a relationship between the variables. C. Do not reject the null hypothesis and conclude the evidence is not strong enough to show a relationship between the two variables. D. Do not reject the null hypothesis and conclude there is a relationship between the variables. 30

5 Questions 4 to 8: In the General Social Survey, respondents were asked If your party nominated a woman for President, would you vote for her if she were qualified for the job? Minitab output for 953 respondents, by race, is shown below: Expected counts are printed below observed counts white black other Total yes no Total Chi-Sq = = P-Value = What is the null hypothesis for this situation? A. There is a relationship between race and opinion on voting for a female president in the sample. B. There is no relationship between race and opinion on voting for a female president in the sample. C. There is a relationship between race and opinion on voting for a female president in the population. D. There is no relationship between race and opinion on voting for a female president in the population. 5. What is the alternative hypothesis for this situation? A. There is a relationship between race and opinion on voting for a female president in the sample. B. There is no relationship between race and opinion on voting for a female president in the sample. C. There is a relationship between race and opinion on voting for a female president in the population. D. There is no relationship between race and opinion on voting for a female president in the population. 6. What is the value of the test statistic? A. 953 B C What are the degrees of freedom for the test statistic? A. B. 3 C At a significance level of 0.05, what is the conclusion? A. Reject the null hypothesis and conclude there is no relationship between the variables. B. Reject the null hypothesis and conclude there is a relationship between the variables. C. Do not reject the null hypothesis and conclude the evidence is not strong enough to show a relationship between the two variables. D. Do not reject the null hypothesis and conclude there is a relationship between the variables. 31

6 9. A sociologist uses a z-test to examine the difference between the proportions of men and women opposed to capital punishment. The value of the z-statistic is z = 4. Suppose the sociologist had instead used a chi-square test to analyze the data. What would be the value of the chi-square statistic? A. B. 4 C. 16 D. Not enough information is given to determine the value. Questions 30 to 33: A researcher conducted a study on college students to see if there was a link between gender and how often they have cheated on an exam. She asked two questions on a survey: (1) What is your gender? Male Female () How many times have you cheated on an exam while in college? Never 1 or times 3 or more times A two-way table of observed counts follows: Cheated on an exam? Gender Never 1 or times 3 or more times Total Male Female Total Considering the researcher s objectives, what is the appropriate null hypothesis to test? A. p = 0.50 where p = probability of answering "Never" to question () on the survey. B. There is a difference between males and females with regard to the distribution of responses. C. There is no relationship between the two variables. D. There is a relationship between the two variables. 31. What are the degrees of freedom for the test statistic? A. 6 B. 5 C. 3 D. 3. How many female students would you expect to have cheated once or twice if the null hypothesis were true? A. 0 B. 5 C. 30 D The value of the χ -test statistic is Are the results statistically significant at the 5% significance level? A. Yes, because 5.33 is greater than the critical value of B. Yes, because 5.33 is greater than the critical value of C. No, because 5.33 is smaller than the critical value of D. No, because 5.33 is smaller than the critical value of

7 Questions 34 to 37: Is there a relationship between the color of one's eyes and the comparative lengths of one's index and ring fingers? Students were asked "which finger is longer: your index finger or your ring finger? Or are they the same?" They also reported the color of their eyes (blue, brown, green, or hazel). The analysis of the results is given below. Expected counts are printed below observed counts Comparison of finger lengths Same 'Index' 'Ring' Total Longer Longer blue brown green hazel Total P-Value = What is the appropriate statistical technique to analyze the data? A. A chi-square test for association. B. A chi-square goodness-of-fit test. C. A two-sample t-test. D. Analysis of variance. 35. From the analysis shown, what can we conclude at the 10%significance level? A. There is a statistically significant relationship between eye color and the comparative length of the index and ring fingers. B. There is no statistically significant relationship between eye color and the comparative length of the index and ring fingers. C. There is insufficient information given because the degrees of freedom of the test statistic are not specified. D. There is a statistically significant relationship between eye color and the comparative length of the index and ring fingers for some eye colors but not for others. 36. What are the degrees of freedom for this test? A. B. 3 C. 6 D What is the expected count for "blue eyes" and "same"? A. 59/3 B. 9/4 C. 9/1 D. (59)(9)/9 33

8 Questions 38 to 41: In the 1994 General Social Survey, a nationwide survey done every other year in the United States, the 1,185 respondents who had ever been married were asked the age at which they first wed and whether they had ever been divorced. The two-way table below summarizes the observed counts for the relationship between age first wed (categorized into four age groups) and ever divorce (no or yes). A chi-square value and p- value are given below the table. Rows: Age First Wed Columns: Ever Divorced No Yes All Under All Chi-Square = 44.00, DF =, P-Value = What is the appropriate null hypothesis for this table? A. In the sample, there is a relationship between age first wed and ever divorced. B. In the population represented by the sample, there is a relationship between age first wed and ever divorced. C. In the sample, there is no relationship between age first wed and ever divorced. D. In the population represented by the sample, there is no relationship between age first wed and ever divorced. 39. The p-value is given as This value was calculated as A. the area to the right of under a chi-square distribution with df = 3. B. the area to the right of under a chi-square distribution with df = 8. C. the area to the left of under a chi-square distribution with df = 3. D. the area to the left of under a chi-square distribution with df = What is the expected count for the Under 0 and No cell? A. (33)(1/3) B. 150 C. (33)(7)/1185 D. (1185)(1/8) 41. Among those first wed under the age of 0, what proportion has ever been divorced? A. 173/1185 B. 173/463 C. 173/150 D. 173/33 34

9 Questions 4 to 45: Students in a statistics class were asked, With whom do you find it easier to make friends: person of the same sex, person of opposite sex, or no preference? A table summarizing the responses by gender is given below. Minitab results for a chi-square test for these data were Chi-Sq = 7.15 p-value = With whom is it easier to make friends? Gender no preference opposite sex same sex Total Male Female Total What is the null hypothesis for this situation? A. The variables gender and with whom is it easier to make friends? are dependent in the population. B. There is a relationship between gender and whom it is easier to make friends with in the population. C. The distribution of the answers to the question with whom is it easier to make friends? for male students differ from that of the female students. D. There is no relationship between gender and whom it is easier to make friends with in the population. 43. What percentage of female students think it is easier to make friends with a girl? A. 15% B. 5% C. 30% D. 60% 44. What is the expected number of female students who think it is easier to make friends with a girl, if the null hypothesis were true? A. 0 B. 5 C. 30 D What are the degrees of freedom for this situation? A. B. 3 C. 4 D. 5 35

10 Questions 46 to 5: In the General Social Survey, respondents were asked if they agreed with the following statement: In spite of what some people say, the lot (situation/condition) of the average man is getting worse, not better. Minitab output, summarizing the results for 989 respondents by race, is shown below: Expected counts are printed below observed counts white black other Total agree disagree Total Chi-Sq = = P-Value = State the null hypothesis and alternative hypotheses. KEY: Null hypothesis: There is no relationship between race and belief that the lot of the average man is getting worse. Alternative hypothesis: There is a relationship between race and belief. 47. What is the percentage of white respondents who agree that the human lot is getting worse? KEY: Percentage of Whites = 476/850 = 56%. 48. What is the percentage of black respondents who agree that the human lot is getting worse? KEY: Percentage of Blacks = 86/101 = 85%. 49. What is the value of the test statistic? KEY: Test statistic = What are the degrees of freedom? egrees of freedom =. 51. What is the p-value or p-value range? KEY: p-value < (p-value = in the Minitab output). 5. At a significance level of 0.05, what is the conclusion? KEY: Reject the null hypothesis and conclude that there seems to be a relationship between race and belief that the lot of the average man is getting worse. 36

11 Questions 53 to 59: A randomly selected group 78 seniors is asked about their plans after graduation. Is there a relationship between the gender of the students and what they plan to do when they graduate from college? SPSS was used to analyze the data. Part of the output is shown below: 53. State the null hypothesis and alternative hypotheses. KEY: Null hypothesis: There is no relationship between gender and after college plans in the population of all college seniors. Alternative hypothesis: There is a relationship between gender and after college plans in the population of all college seniors. 54. What percentage of male students plan to take a year off? KEY: Percentage = 9/43 = 0.9% 55. What percentage of female students are planning to go to graduate school? KEY: Percentage = 13/35 = 37.1% 56. What is the expected number of female students going to graduate school under the null hypothesis? KEY: What are the degrees of freedom for this test? KEY: df = (3 1)( 1) = 58. Another part of the output is shown below: What is the p-value or p-value range? KEY: 0.5 < p-value < 0.50 (or p-value = 0.9). 59. At a significance level of 0.10, what is the conclusion? KEY: The results are not significant. We may conclude that there does not seem to be a relationship between gender and after college plans in the population of all college seniors represented by this sample. 37

12 Questions 60 to 66: The table below shows the counts by gender and highest degree attained for 498 respondents in the General Social Survey. Highest Degree Gender No High School Degree High School Degree Junior College Bachelor Degree Graduate Degree Total Male Female Total State the null hypothesis and alternative hypotheses. KEY: Null hypothesis: There is no relationship between gender and highest degree in the population. Alternative hypothesis: There is a relationship between gender and highest degree in the population. 61. What percentage of male respondents has more than just a high school degree? KEY: Percentage = ( )/17 = 33.6% 6. What percentage of female respondents has a graduate degree? KEY: Percentage = 1/81 = 4.3% 63. What is the expected number of female respondents with a graduate degree under the null hypothesis? KEY: What is the contribution to the chi-square statistic of the cell female respondents with a graduate degree? KEY: What are the degrees of freedom for this test? KEY: df = (5 1)( 1) = Contributions to the chi-square test statistic of 4 cells are greater than 3. With this information, what do you already know about the p-value? KEY: p-value <

13 Section 15. Questions 67 to 70: In the General Social Survey, respondents were asked If your party nominated a woman for President, would you vote for her if she were qualified for the job? A two-way table summarizing the results for 953 respondents, by gender, is shown below: Vote for female candidate? Gender Yes No Total Female Male Total If the null hypothesis of equal proportions of Yes votes for males and females were true, what is the expected number of females in the sample who would give a Yes response to having a female president? A B C If the null hypothesis were true, what is the expected number of females in the sample who would give a No response to having a female president? A B C The chi-square test statistic = What is the p-value or p-value range? A < p-value < 0.05 B < p-value < 0.05 C < p-value < At a significance level of 0.05, what is your conclusion? A. The null hypothesis is rejected: the relationship between gender and support for a female president is statistically significant. B. The null hypothesis is rejected: the relationship between gender and support for a female president is not statistically significant. C. The null hypothesis is not rejected: the relationship between gender and support for a female president is statistically significant. D. The null hypothesis is not rejected: the relationship between gender and support for a female president is not statistically significant. 39

14 Questions 71 to 74: In the General Social Survey, respondents were asked Do you favor or oppose the death penalty for persons convicted of murder? A two-way table summarizing the results for 1447 respondents, by gender, is shown below: Favor or oppose death penalty? Gender Favor Oppose Total Female Male Total If the null hypothesis of equal proportions of Favor responses for males and females were true, what is the expected number of females in the sample who would favor the death penalty? A B C If the null hypothesis were true, what is the expected number of males in the sample who would favor the death penalty? A B C The chi-square test statistic = 0.9. What is the p-value or p-value range? A. p-value < B < p-value < C < p-value < At a significance level of 0.05, what is your conclusion? A. The null hypothesis is rejected: the relationship between gender and support for death penalty is statistically significant. B. The null hypothesis is rejected: the relationship between gender and support for death penalty is not statistically significant. C. The null hypothesis is not rejected: the relationship between gender and support for death penalty is statistically significant. D. The null hypothesis is not rejected: the relationship between gender and support for death penalty is not statistically significant. 330

15 Questions 75 to 78: In the General Social Survey, respondents were asked Would you approve of an adult male punching a stranger if the stranger was drunk and bumped into the man and his wife on the street? A two-way table summarizing the results for 1006 respondents, by gender, is shown below: Would you approve of punch? Gender Yes No Total Female Male Total If the null hypothesis of equal proportions of Yes votes for males and females were true, what is the expected number of females in the sample who think it would be all right to punch a drunken stranger? A B C If the null hypothesis were true, what is the expected number of males in the sample who think it would be all right to punch a drunken stranger? A B C The chi-square test statistic = What is the p-value or p-value range? A. p-value = 0.00 B. p-value < C. p-value > At a significance level of 0.05, what is your conclusion? A. The null hypothesis is rejected: the relationship between gender and approval for punching is statistically significant. B. The null hypothesis is rejected: the relationship between gender and approval for punching is not statistically significant. C. The null hypothesis is not rejected: the relationship between gender and approval for punching is statistically significant. D. The null hypothesis is not rejected: the relationship between gender and approval for punching is not statistically significant. 331

16 Questions 79 to 83: In the General Social Survey, respondents were asked, Do you agree with the following statement? In spite of what some people say, the lot (situation/condition) of the average man is getting worse, not better. The results, for 989 respondents by gender, are shown below. Lot is getting worse Gender Agree Disagree Total Female Male Total What are the null and alternative hypotheses? KEY: Null hypothesis: There is no difference between the population proportions of men and women who believe that the lot of the average man is getting worse. Alternative hypothesis: There is a difference between the population proportions of men and women who believe that the lot of the average man is getting worse. 80. If the null hypothesis were true, what is the expected number of women in the sample who agree that the lot of the average man is getting worse? KEY: If the null hypothesis were true, what is the expected number of men in the sample who agree that the lot of the average man is getting worse? KEY: The chi-square test statistic = What is the p-value or p-value range? KEY: < p-value < or p-value = At a significance level of 0.05, what is your conclusion? KEY: There is a statistically significant difference between the proportions of men and women in the population who agree that the human lot is getting worse. Questions 84 to 86: A group of 3 rd grade students is given a craft project to take home. Half of the children received an instruction sheet with the project that included photos of examples. The other half of the children were just given general (verbal) instructions from the teacher. At the end of the project the children were asked if they enjoyed doing the project. Enjoyed project Instructions Yes No Total Written Verbal Total If the null hypothesis (that there is no association between the type of instruction and the enjoyment of the children in the population) were true, what is the expected number of children in the sample who received verbal instructions and enjoyed the project? KEY: What is the value of the test statistic? KEY: Are the results statistically significant at α = 0.05? t df = 1, we have a critical value of The test statistic of.14 is not greater than the critical value, so we do not reject the null hypothesis (p-value > 0.05). 33

17 Questions 87 to 90: The table below shows the opinions of 908 respondents in the General Social Survey to the question Do you believe there is life after death? Life After Death? Gender Yes No Total Male Female Total If the null hypothesis (that there is no association between gender and believing in life after death) were true, what is the expected number of male respondents who believe in life after death? KEY: If the null hypothesis (that there is no association between gender and believing in life after death) were true, what is the expected number of female respondents who believe in life after death? KEY: What is the value of the test statistic? KEY: Are the results statistically significant at α = 0.05? t df = 1, we have a critical value of 3.84 and 5.63 is greater than the critical value, so we reject the null hypothesis (p-value < 0.05). Questions 91 to 94: The table below shows the responses from a sample of 680 people in the General Social Survey to the question, Do you sometimes drink more than you think you should? Drink more than should? Gender Yes No Total Male Female Total If the null hypothesis (that there is no association between gender and drinking more than one should) were true, what is the expected number of male respondents who drink more than they should? KEY: If the null hypothesis (that there is no association between gender and drinking more than one should) were true, what is the expected number of female respondents who drink more than they should? KEY: What is the value of the test statistic? KEY: Are the results statistically significant at α =.01? t df = 1, we have a critical value of 6.63 and 9.3 is much greater than the critical value, so we reject the null hypothesis (p-value < 0.01; we even know that p-value < 0.001). 333

19 Questions 100 to 105: A gambler wanted to test whether or not a die was fair. He rolled the die 180 times and got the results shown below. For example, the number 1 appeared on 40 rolls. Die Result Total Count What is the null hypothesis for this chi-square goodness of fit test? A. The probabilities of a 1,,, 6 are 40/180, 40/180,, 0/180, respectively. B. The die is not fair: the probabilities of getting a particular number (e.g. 1 ) are not all equal. C. The die is fair: the probability of getting any particular number (e.g. 1 ) is 1/ If the die is fair, what is the expected number of times the number 1 should appear in 180 rolls of the die? A. 40 B. 30 C What are the degrees of freedom for the chi-square goodness of fit statistic? A. 6 B. 5 C What is the value for the goodness of fit chi-square statistic? A B C What is the p-value range? A. p-value < B < p-value < 0.05 C < p-value < At a significance level of 0.05, what is your conclusion? A. The null hypothesis is rejected: the die does not seem to be fair. B. The null hypothesis is rejected: the die appears to be fair. C. The null hypothesis is not rejected: there is insufficient evidence to conclude the die is not fair. D. The null hypothesis is not rejected: there is sufficient evidence to conclude the die is fair. 335

20 Questions 106 to 111: A student wants to test a claim made by a pizza company. The claim is that the proportion of students whose favorite pizza is pepperoni is 40%, vegetarian is 40%, and all others is 0%. The student takes a random sample of 100 students, and obtained the following results. Favorite Pizza Pepperoni Vegetarian Other Total Number of Students What are the null and alternative hypotheses for a chi-square goodness of fit test? KEY: Null hypothesis: The population proportion of students whose favorite pizza is pepperoni, vegetarian, and others is what the company claims: i.e. 40%, 40%, and 0%, respectively. Alternative hypothesis: the population proportions are not 40%, 40%, and 0% What are the degrees of freedom for the chi-square goodness of fit test? KEY: degrees of freedom If the null hypothesis were true, what are the expected numbers of students in the sample whose favorite pizza is pepperoni, vegetarian, or other? KEY: 40 students (Pepperoni); 40 students (Vegetarian); 0 students (Other) 109. What is the value of the chi-square goodness of fit statistic? KEY: What is the p-value or p-value range? KEY: p-value > 0.50 or p-value = At a significance level of 0.05, what is the conclusion? KEY: The evidence is not strong enough to reject the company s claim that the proportions of favorite pizzas for pepperoni, vegetarian, and other are 40%, 40%, and 0%, respectively. 336

21 Questions 11 to 117: At entrance C of the football stadium there are 3 swing gates for the spectators. On football Saturday, two high school students sit at this entrance and count the number of people who enter through each of the swing gates for an hour. On Monday, during their statistics class, they wish to determine if the percentages of people who use each of the three gates on football Saturday are equal. The data they collected during the hour on football Saturday is shown below. Swing gate Left gate Middle gate Right gate Total Number of spectators What are the null and alternative hypotheses for a chi-square goodness of fit test? KEY: Null hypothesis: The population proportions of spectators who use each of the three gates are equal, i.e. 1/3. Alternative hypothesis: the population proportions are not all equal to 1/3% What are the degrees of freedom for the chi-square goodness of fit test? KEY: df = 114. If the null hypothesis were true, what are the expected numbers of spectators in the sample for each gate? KEY: 133/3 = What is the value of the chi-square goodness of fit statistic? KEY: What is the p-value or p-value range? KEY: 0.01 < p-value < 0.05 or p-value = At a significance level of 0.05, what is the conclusion? KEY: The results were significant, so it does not seem that the three gates are being used equally often by the population of spectators represented by this sample. 337

22 338

### Mind on Statistics. Chapter 4

Mind on Statistics Chapter 4 Sections 4.1 Questions 1 to 4: The table below shows the counts by gender and highest degree attained for 498 respondents in the General Social Survey. Highest Degree Gender

### Mind on Statistics. Chapter 13

Mind on Statistics Chapter 13 Sections 13.1-13.2 1. Which statement is not true about hypothesis tests? A. Hypothesis tests are only valid when the sample is representative of the population for the question

### Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)

Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the

### Elementary Statistics

lementary Statistics Chap10 Dr. Ghamsary Page 1 lementary Statistics M. Ghamsary, Ph.D. Chapter 10 Chi-square Test for Goodness of fit and Contingency tables lementary Statistics Chap10 Dr. Ghamsary Page

### Is it statistically significant? The chi-square test

UAS Conference Series 2013/14 Is it statistically significant? The chi-square test Dr Gosia Turner Student Data Management and Analysis 14 September 2010 Page 1 Why chi-square? Tests whether two categorical

### 14 Chi-Square CHAPTER Chapter Outline 14.1 THE GOODNESS-OF-FIT TEST 14.2 TEST OF INDEPENDENCE

www.ck12.org CHAPTER 14 Chi-Square Chapter Outline 14.1 THE GOODNESS-OF-FIT TEST 14.2 TEST OF INDEPENDENCE 278 www.ck12.org Chapter 14. Chi-Square 14.1 The Goodness-of-Fit Test Learning Objectives Learn

### Mind on Statistics. Chapter 10

Mind on Statistics Chapter 10 Section 10.1 Questions 1 to 4: Some statistical procedures move from population to sample; some move from sample to population. For each of the following procedures, determine

### CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS

CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS Hypothesis 1: People are resistant to the technological change in the security system of the organization. Hypothesis 2: information hacked and misused. Lack

### Math 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2

Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable

### STP231 Brief Class Notes Ch10: Chi-square Tests, Instructor: Ela Jackiewicz

Chi-square Tests for categorical variables Tests of independence: We will consider two situations: A) one variable with r categories in c independent samples from different populations or B) 2 variables

### The Goodness-of-Fit Test

on the Lecture 49 Section 14.3 Hampden-Sydney College Tue, Apr 21, 2009 Outline 1 on the 2 3 on the 4 5 Hypotheses on the (Steps 1 and 2) (1) H 0 : H 1 : H 0 is false. (2) α = 0.05. p 1 = 0.24 p 2 = 0.20

### The Chi-Square Goodness-of-Fit Test, Equal Proportions

Chapter 11 Chi-Square Tests 1 Chi-Square Tests Chapter 11 The Chi-Square Goodness-of-Fit Test, Equal Proportions A hospital wants to know if the proportion of births are the same for each day of the week.

### An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS

The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10- TWO-SAMPLE TESTS Practice

### AP STATISTICS (Warm-Up Exercises)

AP STATISTICS (Warm-Up Exercises) 1. Describe the distribution of ages in a city: 2. Graph a box plot on your calculator for the following test scores: {90, 80, 96, 54, 80, 95, 100, 75, 87, 62, 65, 85,

### 13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations.

13.2 The Chi Square Test for Homogeneity of Populations The setting: Used to compare distribution of proportions in two or more populations. Data is organized in a two way table Explanatory variable (Treatments)

### Math 108 Exam 3 Solutions Spring 00

Math 108 Exam 3 Solutions Spring 00 1. An ecologist studying acid rain takes measurements of the ph in 12 randomly selected Adirondack lakes. The results are as follows: 3.0 6.5 5.0 4.2 5.5 4.7 3.4 6.8

### Example 11-3, pg. 495 The Chi-Square Goodness-of-Fit Test

132 Chapter 11 Chi-Square Tests Chi-Square Tests Chapter 11 Section 11.2 Example 11-3, pg. 495 The Chi-Square Goodness-of-Fit Test A bank manager wanted to investigate if the percentage of people who use

### Using Stata for Categorical Data Analysis

Using Stata for Categorical Data Analysis NOTE: These problems make extensive use of Nick Cox s tab_chi, which is actually a collection of routines, and Adrian Mander s ipf command. From within Stata,

### Lecture 42 Section 14.3. Tue, Apr 8, 2008

the Lecture 42 Section 14.3 Hampden-Sydney College Tue, Apr 8, 2008 Outline the 1 2 the 3 4 5 the The will compute χ 2 areas, but not χ 2 percentiles. (That s ok.) After performing the χ 2 test by hand,

### Math 225. Chi-Square Tests. 1. A Chi-Square Goodness-of-Fit Test. Conditions. Chi-Square Distribution. The Test Statistic

Chi-Square Tests Math 5 Chapter 11 In this chapter, you will learn about two chi-square tests: Goodness of fit. Are the proportions of the different outcomes in this population equal to the hypothesized

Chapter 11 Testing Hypotheses About Proportions Hypothesis testing method: uses data from a sample to judge whether or not a statement about a population may be true. Steps in Any Hypothesis Test 1. Determine

### Mind on Statistics. Chapter 12

Mind on Statistics Chapter 12 Sections 12.1 Questions 1 to 6: For each statement, determine if the statement is a typical null hypothesis (H 0 ) or alternative hypothesis (H a ). 1. There is no difference

### Chi-Square Tests TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson

Math Objectives Students will recognize that chi-squared tests are for counts of categorical data. Students will identify the appropriate chi-squared test to use for a given situation: 2 Goodness of Fit

### The Chi Square Test. Diana Mindrila, Ph.D. Phoebe Balentyne, M.Ed. Based on Chapter 23 of The Basic Practice of Statistics (6 th ed.

The Chi Square Test Diana Mindrila, Ph.D. Phoebe Balentyne, M.Ed. Based on Chapter 23 of The Basic Practice of Statistics (6 th ed.) Concepts: Two-Way Tables The Problem of Multiple Comparisons Expected

### Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation

Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.

### CHAPTER 11: FACTS ABOUT THE CHI- SQUARE DISTRIBUTION

CHAPTER 11: FACTS ABOUT THE CHI- SQUARE DISTRIBUTION Exercise 1. If the number of degrees of freedom for a chi-square distribution is 25, what is the population mean and standard deviation? mean = 25 and

### Chi-Square Test for Qualitative Data

Chi-Square Test for Qualitative Data For qualitative data (measured on a nominal scale) * Observations MUST be independent - No more than one measurement per subject * Sample size must be large enough

### The Chi-Square Test. STAT E-50 Introduction to Statistics

STAT -50 Introduction to Statistics The Chi-Square Test The Chi-square test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed

### Mind on Statistics. Chapter 8

Mind on Statistics Chapter 8 Sections 8.1-8.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable

### Module 9: Nonparametric Tests. The Applied Research Center

Module 9: Nonparametric Tests The Applied Research Center Module 9 Overview } Nonparametric Tests } Parametric vs. Nonparametric Tests } Restrictions of Nonparametric Tests } One-Sample Chi-Square Test

### MATH Chapter 23 April 15 and 17, 2013 page 1 of 8 CHAPTER 23: COMPARING TWO CATEGORICAL VARIABLES THE CHI-SQUARE TEST

MATH 1342. Chapter 23 April 15 and 17, 2013 page 1 of 8 CHAPTER 23: COMPARING TWO CATEGORICAL VARIABLES THE CHI-SQUARE TEST Relationships: Categorical Variables Chapter 21: compare proportions of successes

### CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY

CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY The hypothesis testing statistics detailed thus far in this text have all been designed to allow comparison of the means of two or more samples

### SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Ch. 10 Chi SquareTests and the F-Distribution 10.1 Goodness of Fit 1 Find Expected Frequencies Provide an appropriate response. 1) The frequency distribution shows the ages for a sample of 100 employees.

### SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS)

SPSS on two independent samples. Two sample test with proportions. Paired t-test (with more SPSS) State of the course address: The Final exam is Aug 9, 3:30pm 6:30pm in B9201 in the Burnaby Campus. (One

### Objectives. 9.1, 9.2 Inference for two-way tables. The hypothesis: no association. Expected cell counts. The chi-square test.

Objectives 9.1, 9.2 Inference for two-way tables The hypothesis: no association Expected cell counts The chi-square test Using software Further reading: http://onlinestatbook.com/2/chi_square/contingency.html

### Review #2. Statistics

Review #2 Statistics Find the mean of the given probability distribution. 1) x P(x) 0 0.19 1 0.37 2 0.16 3 0.26 4 0.02 A) 1.64 B) 1.45 C) 1.55 D) 1.74 2) The number of golf balls ordered by customers of

### Chi-Square Tests and the F-Distribution. Goodness of Fit Multinomial Experiments. Chapter 10

Chapter 0 Chi-Square Tests and the F-Distribution 0 Goodness of Fit Multinomial xperiments A multinomial experiment is a probability experiment consisting of a fixed number of trials in which there are

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Open book and note Calculator OK Multiple Choice 1 point each MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data.

### Unit 29 Chi-Square Goodness-of-Fit Test

Unit 29 Chi-Square Goodness-of-Fit Test Objectives: To perform the chi-square hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni

### Introduction to Hypothesis Testing. Copyright 2014 Pearson Education, Inc. 9-1

Introduction to Hypothesis Testing 9-1 Learning Outcomes Outcome 1. Formulate null and alternative hypotheses for applications involving a single population mean or proportion. Outcome 2. Know what Type

### Example for testing one population mean:

Today: Sections 13.1 to 13.3 ANNOUNCEMENTS: We will finish hypothesis testing for the 5 situations today. See pages 586-587 (end of Chapter 13) for a summary table. Quiz for week 8 starts Wed, ends Monday

### General Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test

Five types of statistical analysis General Procedure for Hypothesis Test Descriptive Inferential Differences Associative Predictive What are the characteristics of the respondents? What are the characteristics

### Chi Square Distribution

17. Chi Square A. Chi Square Distribution B. One-Way Tables C. Contingency Tables D. Exercises Chi Square is a distribution that has proven to be particularly useful in statistics. The first section describes

### Statistics Review PSY379

Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses

### Hypothesis Testing for a Proportion

Math 122 Intro to Stats Chapter 6 Semester II, 2015-16 Inference for Categorical Data Hypothesis Testing for a Proportion In a survey, 1864 out of 2246 randomly selected adults said texting while driving

### Chi Square for Contingency Tables

2 x 2 Case Chi Square for Contingency Tables A test for p 1 = p 2 We have learned a confidence interval for p 1 p 2, the difference in the population proportions. We want a hypothesis testing procedure

### STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4

STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate

### Hypothesis Testing for Categorical Data

Hypothesis Testing for Categorical Data 1. A die is rolled 36 times, with the following results: VALUE 1 2 3 4 5 6 TIMES 8 1 7 9 5 6 Is the die fair? Perform a Hypothesis Test with α =.05. Step One: H

### IB Practice Chi Squared Test of Independence

1. A university required all Science students to study one language for one year. A survey was carried out at the university amongst the 150 Science students. These students all studied one of either French,

### Chi-Square Tests. In This Chapter BONUS CHAPTER

BONUS CHAPTER Chi-Square Tests In the previous chapters, we explored the wonderful world of hypothesis testing as we compared means and proportions of one, two, three, and more populations, making an educated

### People like to clump things into categories. Virtually every research

05-Elliott-4987.qxd 7/18/2006 5:26 PM Page 113 5 Analysis of Categorical Data People like to clump things into categories. Virtually every research project categorizes some of its observations into neat,

### C. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters.

Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample

### Provide an appropriate response. Solve the problem. Determine the null and alternative hypotheses for the proposed hypothesis test.

Provide an appropriate response. 1) Suppose that x is a normally distributed variable on each of two populations. Independent samples of sizes n1 and n2, respectively, are selected from the two populations.

### Introduction to Hypothesis Testing. Point estimation and confidence intervals are useful statistical inference procedures.

Introduction to Hypothesis Testing Point estimation and confidence intervals are useful statistical inference procedures. Another type of inference is used frequently used concerns tests of hypotheses.

### MATH 10: Elementary Statistics and Probability Chapter 11: The Chi-Square Distribution

MATH 10: Elementary Statistics and Probability Chapter 11: The Chi-Square Distribution Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of slides,

### Using Excel in Research. Hui Bian Office for Faculty Excellence

Using Excel in Research Hui Bian Office for Faculty Excellence Data entry in Excel Directly type information into the cells Enter data using Form Command: File > Options 2 Data entry in Excel Tool bar:

### Hypothesis Testing. Male Female

Hypothesis Testing Below is a sample data set that we will be using for today s exercise. It lists the heights for 10 men and 1 women collected at Truman State University. The data will be entered in the

### Statistics 2014 Scoring Guidelines

AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home

### Chi-Square. The goodness-of-fit test involves a single (1) independent variable. The test for independence involves 2 or more independent variables.

Chi-Square Parametric statistics, such as r and t, rest on estimates of population parameters (x for μ and s for σ ) and require assumptions about population distributions (in most cases normality) for

### Testing Hypotheses using SPSS

Is the mean hourly rate of male workers \$2.00? T-Test One-Sample Statistics Std. Error N Mean Std. Deviation Mean 2997 2.0522 6.6282.2 One-Sample Test Test Value = 2 95% Confidence Interval Mean of the

### CHI SQUARE DISTRIBUTION

CI SQUARE DISTRIBUTION 1 Introduction to the Chi Square Test of Independence This test is used to analyse the relationship between two sets of discrete data. Contingency tables are used to examine the

### CATEGORICAL DATA Chi-Square Tests for Univariate Data

CATEGORICAL DATA Chi-Square Tests For Univariate Data 1 CATEGORICAL DATA Chi-Square Tests for Univariate Data Recall that a categorical variable is one in which the possible values are categories or groupings.

### The Effects of Alcohol Use on Academic Performance Among College Students

The Effects of Alcohol Use on Academic Performance Among College Students Jill Coyman ABSTRACT This study examines college students alcohol use and how it affects their academic performance, specifically

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

### Name: Date: Use the following to answer questions 3-4:

Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin

### CHAPTER 9 HYPOTHESIS TESTING

CHAPTER 9 HYPOTHESIS TESTING The TI-83 Plus and TI-84 Plus fully support hypothesis testing. Use the key, then highlight TESTS. The options used in Chapter 9 are given on the two screens. TESTING A SINGLE

### Analysis of categorical data: Course quiz instructions for SPSS

Analysis of categorical data: Course quiz instructions for SPSS The dataset Please download the Online sales dataset from the Download pod in the Course quiz resources screen. The filename is smr_bus_acd_clo_quiz_online_250.xls.

### Chi Square Goodness of Fit & Two-way Tables (Create) MATH NSPIRED

Overview In this activity, you will look at a setting that involves categorical data and determine which is the appropriate chi-square test to use. You will input data into a list or matrix and conduct

### 12.5: CHI-SQUARE GOODNESS OF FIT TESTS

125: Chi-Square Goodness of Fit Tests CD12-1 125: CHI-SQUARE GOODNESS OF FIT TESTS In this section, the χ 2 distribution is used for testing the goodness of fit of a set of data to a specific probability

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) ±1.88 B) ±1.645 C) ±1.96 D) ±2.

Ch. 6 Confidence Intervals 6.1 Confidence Intervals for the Mean (Large Samples) 1 Find a Critical Value 1) Find the critical value zc that corresponds to a 94% confidence level. A) ±1.88 B) ±1.645 C)

### Mind on Statistics. Chapter 16 Section Chapter 16

Mind on Statistics Chapter 16 Section 16.1 1. Which of the following is not one of the assumptions made in the analysis of variance? A. Each sample is an independent random sample. B. The distribution

### Two-Way Tables. Lesson 16. Main Idea. New Vocabulary two-way table relative frequency

Lesson 16 Main Idea Construct and interpret two-way tables. New Vocabulary two-way table relative frequency Math Online glencoe.com Two-Way Tables SCHOOL The data from a survey of 50 students is shown

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Ch. 4 Discrete Probability Distributions 4.1 Probability Distributions 1 Decide if a Random Variable is Discrete or Continuous 1) State whether the variable is discrete or continuous. The number of cups

### p1^ = 0.18 p2^ = 0.12 A) 0.150 B) 0.387 C) 0.300 D) 0.188 3) n 1 = 570 n 2 = 1992 x 1 = 143 x 2 = 550 A) 0.270 B) 0.541 C) 0.520 D) 0.

Practice for chapter 9 and 10 Disclaimer: the actual exam does not mirror this. This is meant for practicing questions only. The actual exam in not multiple choice. Find the number of successes x suggested

### STA 2023H Solutions for Practice Test 4

1. Which statement is not true about confidence intervals? A. A confidence interval is an interval of values computed from sample data that is likely to include the true population value. B. An approximate

### PASS Sample Size Software

Chapter 250 Introduction The Chi-square test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial

### Association Between Variables

Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi

### t Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon

t-tests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com

### Practice#1(chapter1,2) Name

Practice#1(chapter1,2) Name Solve the problem. 1) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or inferential statistics? A) inferential statistics

### CHAPTER 12. Chi-Square Tests and Nonparametric Tests LEARNING OBJECTIVES. USING STATISTICS @ T.C. Resort Properties

CHAPTER 1 Chi-Square Tests and Nonparametric Tests USING STATISTICS @ T.C. Resort Properties 1.1 CHI-SQUARE TEST FOR THE DIFFERENCE BETWEEN TWO PROPORTIONS (INDEPENDENT SAMPLES) 1. CHI-SQUARE TEST FOR

### 3.4 Statistical inference for 2 populations based on two samples

3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted

### a) Find the five point summary for the home runs of the National League teams. b) What is the mean number of home runs by the American League teams?

1. Phone surveys are sometimes used to rate TV shows. Such a survey records several variables listed below. Which ones of them are categorical and which are quantitative? - the number of people watching

### Independent t- Test (Comparing Two Means)

Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent

### 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

### 3. Analysis of Qualitative Data

3. Analysis of Qualitative Data Inferential Stats, CEC at RUPP Poch Bunnak, Ph.D. Content 1. Hypothesis tests about a population proportion: Binomial test 2. Chi-square testt for goodness offitfit 3. Chi-square

### Carolyn Anderson & Youngshil Paek (Slides created by Shuai Sam Wang) Department of Educational Psychology University of Illinois at Urbana-Champaign

Carolyn Anderson & Youngshil Paek (Slides created by Shuai Sam Wang) Department of Educational Psychology University of Illinois at Urbana-Champaign Key Points 1. Data 2. Variable 3. Types of data 4. Define

### Categorical Data Analysis

Richard L. Scheaffer University of Florida The reference material and many examples for this section are based on Chapter 8, Analyzing Association Between Categorical Variables, from Statistical Methods

### Chapter 10 Analysis of Categorical Variables

Chapter 10 Analysis of Categorical Variables 10.1 Introduction In Chap. 7, we talked about hypothesis testing regarding population proportions. There, we used the central limit theorem (for large enough

### Chapter 7 - Practice Problems 2

Chapter 7 - Practice Problems 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the requested value. 1) A researcher for a car insurance company

### Results from the 2014 AP Statistics Exam. Jessica Utts, University of California, Irvine Chief Reader, AP Statistics jutts@uci.edu

Results from the 2014 AP Statistics Exam Jessica Utts, University of California, Irvine Chief Reader, AP Statistics jutts@uci.edu The six free-response questions Question #1: Extracurricular activities

### Solutions to Homework 10 Statistics 302 Professor Larget

s to Homework 10 Statistics 302 Professor Larget Textbook Exercises 7.14 Rock-Paper-Scissors (Graded for Accurateness) In Data 6.1 on page 367 we see a table, reproduced in the table below that shows the

### SCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES

SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR

### Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Comparing Multiple Proportions, Test of Independence and Goodness of Fit Content Testing the Equality of Population Proportions for Three or More Populations Test of Independence Goodness of Fit Test 2

### TABLE OF CONTENTS. About Chi Squares... 1. What is a CHI SQUARE?... 1. Chi Squares... 1. Hypothesis Testing with Chi Squares... 2

About Chi Squares TABLE OF CONTENTS About Chi Squares... 1 What is a CHI SQUARE?... 1 Chi Squares... 1 Goodness of fit test (One-way χ 2 )... 1 Test of Independence (Two-way χ 2 )... 2 Hypothesis Testing

### Stats Review Chapters 9-10

Stats Review Chapters 9-10 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

### 1. Chi-Squared Tests

1. Chi-Squared Tests We'll now look at how to test statistical hypotheses concerning nominal data, and specifically when nominal data are summarized as tables of frequencies. The tests we will considered

### Chapter 23. Two Categorical Variables: The Chi-Square Test

Chapter 23. Two Categorical Variables: The Chi-Square Test 1 Chapter 23. Two Categorical Variables: The Chi-Square Test Two-Way Tables Note. We quickly review two-way tables with an example. Example. Exercise