Online 19 - Section 11.1-Doug Ensley

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1 Student: Date: Instructor: Doug Ensley Course: MAT Applied Statistics - Ensley Assignment: Online 19 - Section of 16

2 1. The table shown relates political party identification and gender. POLITICAL PARTY IDENTIFICATION GENDER Democrat Independent Republican Total Females Males a. Identify the response variable and the explanatory variable. Gender is the (1) variable. Political party identification is the (2) variable. b. Construct a table showing the conditional distributions of the response variable. Interpret. POLITICAL PARTY IDENTIFICATION GENDER Democrat Independent Republican Total Females % % % 100% Males % % % 100% (Round to one decimal place as needed.) What conclusion can be drawn from the conditional probabilities table? Choose the correct answer below. A. Females are more likely than males to be Democrat and males are more likely than females to be Republican. B. Females are more likely than males to be Republican and males are more likely than females to be Democrat. C. Political party identification appears unrelated to gender. c. Give a hypothetical example of population conditional distributions for which these variables would be independent. POLITICAL PARTY IDENTIFICATION GENDER Democrat Independent Republican Total Females 11.0 % 55.8 % 33.2% 100% Males % % % 100% d. Sketch bar graphs to portray the distributions in (b) and (c). Choose the correct graph for the distribution in (b) below Dem Ind Rep F M F M F M Dem Ind Rep F M F M F M Dem Ind Rep F M F M F M Choose the correct graph for the distribution in (c) below. 2 of Dem Ind Rep F M F M F M Dem Ind Rep F M F M F M Dem Ind Rep F M F M F M

3 (1) explanatory response (2) response explanatory ID: The contingency table shown relates happiness and gender. HAPPINESS GENDER Not too Happy Pretty Happy Very Happy Total Females Males a. Identify the response variable and the explanatory variable. Gender is the (1) Happiness is the (2) variable. variable. b. Construct a table showing the conditional distributions. Interpret. HAPPINESS GENDER Not too Happy Pretty Happy Very Happy Total Females % % % 100% Males % % % 100% (Round to one decimal place as needed.) Choose the correct answer below. A. Females are more likely than males to be very happy and males are more likely than females to be pretty happy. B. Females are more likely than males to be pretty happy and males are more likely than females to be very happy. C. Happiness appears unrelated to gender. c. The population conditional distribution for females is given in the table. What is the population conditional distribution for males if happiness and gender are independent? HAPPINESS GENDER Not too Happy Pretty Happy Very Happy Total Females 11.2 % 55.6 % 33.2% 100% Males % % % 100% (Round your answer to one decimal place.) (1) response explanatory (2) response explanatory ID: of 16

4 3. How large a χ 2 test statistic value provides a P-value of 0.05 for testing independence for the following table dimensions? Complete parts a through e. 1 Click the icon to view the chi-squared distribution table. a. 2 2 The χ 2 test statistic value is (Round to the nearest hundredth as needed.) b. 2 3 The χ 2 test statistic value is (Round to the nearest hundredth as needed.) c. 2 5 The χ 2 test statistic value is (Round to the nearest hundredth as needed.) d. 6 6 The χ 2 test statistic value is (Round to the nearest hundredth as needed.) e. 4 7 The χ 2 test statistic value is (Round to the nearest hundredth as needed.) 1: chi-squared distribution table 4 of 16

5 ID: of 16

6 4. For the given 2 3 table on gender and happiness, software tells us that X 2 = and the P-value = 0.1. Complete parts a and b below. Happiness Gender Not Pretty Very Female Male a. State the null hypothesis ( H 0 ) and alternative hypothesis ( H a ), in context, to which these results apply. Choose the correct answer below. A. H 0 : Gender and happiness are dependent H a : Gender and happiness are independent B. H 0 : Gender and happiness are independent H a : Gender and happiness are dependent C. H 0 : Gender and happiness have equal proportions : Gender and happiness have non-equal proportions H a D. H 0 : P(not happy) = P(pretty happy) = P(very happy) H a : P(not happy) P(pretty happy) P(very happy) b. Interpret the P-value. A. Fail to reject H 0 and conclude that gender and happiness could be independent. B. Reject H 0 and conclude that gender and happiness are not independent. C. Fail to reject H 0 and conclude that gender and happiness are not independent. D. Reject H 0 and conclude that gender and happiness could be independent. ID: of 16

7 5. Subjects who were married were asked about the happiness of their marriage. The given 3 3 table shows the results of the survey. Complete parts a through d. 2 Click the icon to view the chi-squared distribution table. Marital Happiness Income Not Pretty Very Above Average Below a. Determine the null ( H 0 ) and alternative ( H a ) hypotheses for the test. A. H 0 : Income and marital happiness are dependent. H a : Income and marital happiness are independent. B. H 0 : Income and marital happiness are independent. H a : Income and marital happiness are dependent. C. H 0 : Income and marital happiness have a P-value = H a : Income and marital happiness have a P-value D. H 0 : Income and marital happiness have equal proportions. : Income and marital happiness have non-equal proportions. H a b. How large a χ 2 value would give a P-value of exactly 0.025? χ 2 = (Round to two decimal places as needed.) c. The chi-squared statistic for the table equals Find the P-value. A B C D Interpret the P-value. The P-value is the probability of obtaining a χ 2 statistic or larger. The P-value is the probability of obtaining a χ 2 statistic smaller than d. Using a significance level of and the P-value, choose the correct conclusion. A. Reject H 0 and conclude that income and marital happiness are not independent. B. Fail to reject H 0 and conclude that income and marital happiness could be independent. C. Reject H 0 and conclude that income and marital happiness could be independent. D. Fail to reject H 0 and conclude that income and marital happiness are not independent. 2: chi-squared distirubtion table 7 of 16

8 ID: of 16

9 6. According to a study, 897 of 1131 males and 1281 of 1497 females indicated a belief in life after death. Complete parts (a) through (c). a. Construct a contingency table relating gender (categories male and female) as the rows to belief about life after death (categories yes and no) as the columns. BELIEF IN LIFE AFTER DEATH GENDER Yes No Total Males Females b. Find the four expected cell counts for the chi-squared test. BELIEF IN LIFE AFTER DEATH GENDER Yes No Total Males 1131 Females 1497 (Round to the nearest hundredth as needed.) Compare the four expected cell counts to the observed cell counts, identifying cells having more observations than expected. A. There are more men and women who believe in the afterlife than is expected. B. There are more women who believe in the afterlife and men who do not than is expected. C. There are more men who believe in the afterlife and women who do not than is expected. D. There are more men and women who do not believe in the afterlife than is expected. c. Find the X 2 test statistic value to summarize how far the observed cell counts fall from the expected cell counts. The X 2 test statistic value is. (Round to the nearest tenth as needed.) ID: of 16

10 7. The given table refers to a survey in which senior high school students were randomly sampled. It cross-tabulates whether a student had ever smoked cigarettes and whether a student had ever used marijuana. Analyze these data by (a) finding and interpreting conditional distributions with marijuana use as the response variable and (b) reporting all five steps of the chi-squared test of independence. Marijuana Cigarettes Yes No Yes No a. Input each percentage in the table to the right. (Round to one decimal place as needed.) Marijuana Cigarettes Yes No Yes % % No % % Choose the correct interpretation below. A. The data suggest that cigarette use is much more common for those who have smoked marijuana than for those who have not. B. The data suggest that marijuana use is much more common for those who have smoked cigarettes than for those who have not. C. The data suggest that marijuana use is no different for those who have smoked cigarettes than for those who have not. D. The data suggest that cigarette use is no different for those who have smoked marijuana than for those who have not. b. Choose the correct assumptions that are made below. A. There are four categorical variables, randomization was used to obtain the data, and the expected count was at least five in all cells. B. There are two categorical variables, randomization was used to obtain the data, and the expected count was at least ten in all cells. C. There are two categorical variables, randomization was used to obtain the data, and the expected count was at least five in all cells. D. There are four categorical variables, randomization was used to obtain the data, and the expected count was at least ten in all cells. Choose the correct null hypothesis ( H 0 ) and alternative hypothesis ( H a ) below. A. H 0 : Cigarette use and marijuana use are independent. : Cigarette use and marijuana use are dependent. H a B. H 0 : Cigarette use and marijuana use are dependent. : Cigarette use and marijuana use are independent. H a C. H 0 : Cigarette use and marijuana use have a P-value = H a : Cigarette use and marijuana use have a P-value D. H 0 : Cigarette use and marijuana use have equal proportions. : Cigarette use and marijuana use have non-equal proportions. H a Use technology to find the chi-squared test statistic. X 2 = (Round to the nearest integer as needed.) Use technology to find the P-value. (Round to four decimal places as needed.) Use the P-value found above and a significance level of 0.05 to form a conclusion. Choose the correct conclusion below. 10 of 16 A. Fail to reject H 0 and conclude that the two variables are dependent.

11 ID: T 11 of 16

12 8. A study was done in which subjects who had suffered from a stroke were given either placebo or aspirin. Three years later, it was found that 26 of the 678 subjects taking placebo and 22 of the 680 subjects taking aspirin had a heart attack. Use the given information to complete parts a and b. 3 Click the icon to view the chi-squared distribution table. a. Report the data in the form of a 2 2 contingency table. Heart Attack Treatment Yes No Total Placebo Aspirin Total b. Carry out all five steps of the null hypothesis that having a heart attack is independent of whether one takes placebo or aspirin. Choose the correct assumptions that are made. A. There are four categorical variables, randomization was used to obtain the data, and the expected count was at least five in all cells. B. There are two categorical variables, randomization was used to obtain the data, and the expected count was at least ten in all cells. C. There are two categorical variables, randomization was used to obtain the data, and the expected count was at least five in all cells. D. There are four categorical variables, randomization was used to obtain the data, and the expected count was at least ten in all cells. Choose the correct null hypothesis ( H 0 ) and alternative hypothesis ( H a ). A. H 0 : Taking aspirin and having a heart attack have equal proportions. : Taking aspirin and having a heart attack have non-equal proportions. H a B. H 0 : Taking aspirin and having a heart attack have a P-value = H a : Taking aspirin and having a heart attack have a P-value C. H 0 : Taking aspirin and having a heart attack are dependent. : Taking aspirin and having a heart attack are independent. H a D. H 0 : Taking aspirin and having a heart attack are independent. : Taking aspirin and having a heart attack are dependent. H a Calculate the chi-squared test statistic. χ 2 = (Round to three decimal places as needed.) Choose the correct P-value. A B C D Use the P-value found above and a significance level of 0.05 to form a conclusion. 12 of 16 A. Reject H 0 and conclude that the two variables are dependent or associated. B. Reject H 0 and conclude that the two variables could be independent. C. Fail to reject H 0 and conclude that the two variables could be independent.

13 3: chi-squared distribution table ID: of 16

14 1. (1) explanatory (2) response B. Females are more likely than males to be Republican and males are more likely than females to be Democrat Dem Ind Rep F M F M F M Dem Ind Rep F M F M F M 2. (1) explanatory (2) response A. Females are more likely than males to be very happy and males are more likely than females to be pretty happy of

15 B. H 0 : Gender and happiness are independenth a : Gender and happiness are dependent A. Fail to reject H 0 and conclude that gender and happiness could be independent. 5. B. H 0 : Income and marital happiness are independent. H a : Income and marital happiness are dependent B The P-value is the probability of obtaining a χ 2 statistic or larger. B. Fail to reject H 0 and conclude that income and marital happiness could be independent B. There are more women who believe in the afterlife and men who do not than is expected B. The data suggest that marijuana use is much more common for those who have smoked cigarettes than for those who have not. C. There are two categorical variables, randomization was used to obtain the data, and the expected count was at least five in all cells. 15 of 16 A. H 0 : Cigarette use and marijuana use are independent. H a : Cigarette use and marijuana use are dependent. 660

16 B. Reject H 0 and conclude that the two variables are dependent C. There are two categorical variables, randomization was used to obtain the data, and the expected count was at least five in all cells. D. H 0 : Taking aspirin and having a heart attack are independent. H a : Taking aspirin and having a heart attack are dependent B C. Fail to reject H 0 and conclude that the two variables could be independent. 16 of 16

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