Chapter 8 Section 1. Homework A


 Ronald Baldwin
 2 years ago
 Views:
Transcription
1 Chapter 8 Section 1 Homework A 8.7 Can we use the largesample confidence interval? In each of the following circumstances state whether you would use the largesample confidence interval. The variable X denotes the number of observed successes out of n attempts. (a) n = 50, X = 30 (b) n = 90, X = 15. (c) n=10, X = (d) n = 60; X = 50. (e) n = 5, X = What's wrong? Explain what is wrong with each of the following: (a) An approximate 99% confidence interval for an unknown proportion p is ˆp plus or minus its standard error. (c) A significance test is used to evaluate H 0 : ˆp = 0. versus the twosided alternative.
2 8.11 Gambling and college athletics. Gambling is an issue of great concern to those involved in intercollegiate athletics. Because of this, the National Collegiate Athletic Association (NCAA) surveyed studentathletes concerning their gamblingrelated behaviors. 11 There were 5594 Division I male athletes in the survey. Of these, 3547 reported some participation in some gambling behavior. This included playing cards, betting on games of skill, buying lottery tickets, and betting on sports. (a) Find the sample proportion and the largesample margin of error for 95% confidence. Explain in simple terms the meaning of the 95%. Make sure you confirm that you can use the formula that you have used. (b) Because of the way that the study was designed to protect the anonymity of the studentathletes who responded, it was not possible to calculate the number of students who were asked to respond but did not. Does this fact affect the way you interpret the results? Write a short paragraph explaining your answer. (c) In order to use the formula that you used in (a) what did you have to verify is true about the distribution of ˆp? 8.1 Gambling and female athletes. In the study described in the previous exercise, 1447 a total of 3469 female studentathletes re participation in some gambling activity. (a) Use the largesample methods to find an estimate of the true proportion with a 95% confidence interval. ˆp = ( ) = ± (0.4007, )
3 (b) The margin of error for this sample is not same as the margin of error calculated for the previous exercise. Explain why. The margin of error is determined by the value of ˆp and the sample size. In the previous exercise these values were different, thus the reason for a different sample size. 1. Do you enjoy driving your car? In 1991, a Gallup Poll for U.S. population reported this percent to be 79%. (a) The Pew Research Center recently (008) conducted the same poll in the U.S, with n = 50, and 36 reported that they enjoy driving. Does this sample provide evidence that the percent of drivers who enjoy driving their cars has declined since 1991? Make sure you state the null and alternative hypothesis. Report the largesample z statistic and its Pvalue. Verify that you can use the method you used to calculate the pvalue. While the 79% is really a statistic, let us assume for the moment that it is a parameter. 50(0.79) = 39.5 > 10 50(1 0.79) = 10.5 > 10 we can use a normal approximation H 0 : p = 0.79 H a : p < 0.79 ˆp = Test Statistic: Z = (1 0.79) 50 = P( ˆp < 0.7) = P(Z < 1.15) = (b) Draw a sketch of a standard Normal curve mark the location of your z statistic. Shade the appropriate area that corresponds to the Pvalue.
4 (c) The researchers will reject the null hypothesis if ˆp < What is the value 0.66 called? The critical value. (d) What is the probability of a Type I error? P( ˆp < 0.66) = P Z < (1 0.79) 50 = P(Z < .569) = 0.01 (e) The Gallup conducts the same survey (008) in the U.S, with n = 500, and 360 reported that they enjoy driving. Does this sample provide evidence that the percent of drivers who enjoy driving their cars has declined since 1991? Make sure you state the null and alternative hypothesis. Report the largesample z statistic and its Pvalue. Verify that you can use the method you used to calculate the pvalue. 500(0.79) = 395 > (1 0.79) = 105 > 10 we can use a normal approximation H 0 : p = 0.79 H a : p < 0.79 ˆp = Test Statistic: Z = (1 0.79) 500 = P( ˆp < 0.7) = P(Z < ) < (f) Draw a sketch of a standard Normal curve mark the location of your z statistic. Shade the appropriate area that corresponds to the Pvalue. (g) Notice that problem (e) and problem (a) both produced the same ˆp value. What caused the difference in pvalues? While the sample proportion for both problems is the same the sample size is completely different. The increase in sample size makes S.E. phat smaller. Thus, if p is really not 0.79, then whatever the real value of p is, phat will be closer to it than to This is why phat will be further away from 0.79.
5 (h) Create a 95% confidence interval with the data from (e). 0.7 ±1.96 (0.6806, ) 0.7(1 0.7) 500 (i) We want to estimate p, to ± How large of a sample is needed to construct a 95% confidence interval for the proportion of U.S. drivers who enjoy driving their automobiles? Use the estimate found in problem (e) as the value for p *. (0.7)(10.7) = Getting angry at other drivers. Refer to Exercise The same Pew Poll found that 38% of the respondents "shouted, cursed or made gestures to other drivers" in the last year. (b) Does the fact that the respondent is selfreporting these actions affect the way that you interpret the results? Write a short paragraph explaining your answer.. Long sermons. The National Congregations Study collected data in a onehour interview with a key informant that is, a minister, priest, rabbi, or other staff person or leader. ls One question asked concerned the length of the typical sermon. For this question 9 out of 119 congregations reported that the typical sermon lasted more than 30 minutes. (a) Estimate the true proportion for this question with a 95% confidence interval. Notice that I do not have enough successes (need at least 15 successes and failures) to use the large sample confidence interval formula. But I have a sample size large enough, (need at least a sample size of 5), to use the fourplus formula. p = ± ( ) (0.0390, )
6 (b) The respondents to this question were not asked to use a stopwatch to record the lengths of a random sample of sermons at their congregations. They responded based on their impressions of the sermons. Do you think that ministers, priests, rabbis, or other staff persons or leaders might perceive sermon lengths differently from the people listening to the sermons? Discuss how your ideas would influence your interpretation of the results of this study. 3. Confidence level and interval width. Refer to Exercise 1(h). Would a 90% confidence interval be wider or narrower than the one that you found in that exercise? Verify your results by computing the interval. The interval should be narrower, since I am not as confident. 0.7 ±1.645 (0.6869, ) 0.7(1 0.7) Can we use the z test? In each of the following cases state whether or not the Normal approximation to the binomial should be used for a significance test on the population proportion p. (a) n = 30 and Ho: p = 0.. (b) n = 30and Ho: p = 0.6. (c) n = 100 and Ho: p = 0.5. (d) n = 00 and Ho: p = 0.01.
7 8. Instant versus freshbrewed coffee. A matched pairs experiment compares the taste of instant versus freshbrewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 40 subjects who participate in the study, 1 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers freshbrewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer freshbrewed coffee.) (a) Test the claim that a majority of people prefer the taste of freshbrewed coffee. What is the null hypothesis, and alternative hypothesis. Report the largesample z statistic and its Pvalue. Verify that your method used to calculate Pvalue is valid (why do we need to do this?). Let X count the number of people out of 40 that select the freshbrewed coffee. Now I want to show that most people (over half) prefer freshbrewed coffee. Thus, we can not assume that most people prefer freshbrewed coffee. We need a neutral assumption. A neutral assumption is that the preference is the same for instant versus freshbrewed. Let us assume that p = 0.5, that is half of the population prefers freshbrewed coffee over instant, evenly split. The measurement will be those people who said that they preferred freshbrewed. We will try and see if there is any evidence that this proportion is more than 0.5, which would indicate that most people prefer fresh brewed coffee. H 0 : p = 0.5, H a : p > 0.5. ˆp = 8 40 = 0.7 Now we have 8 successes and we have 1 failures, both greater than 10 so we can use a normal approximation Test Statistic: Z = 0.5(0.5) 40 P( ˆp > 0.7) = P(Z >.53) = =.53 The pvalue is , thus the result is statistically significant, meaning we would see a proportion as high as 0.7 or higher (further away from 0.5) when we assume 0.5 is the correct proportion around 57 times out of 10,000 attempts. So our result is rare if 0.5 is true, thus, we wonder why we would see such a value? Of course what we will be more likely to believe is that p is not 0.5 but some other value that is actually larger than 0.5 and that is why we saw a sample proportion of 0.7. We could say that our result is statistically significant at 1%.
8 (b) Draw a sketch of a standard Normal curve and mark the location of your z statistic. Shade the appropriate area that corresponds to the Pvalue. I put the actual binomial curve of the null situation so you can compare to our approximation procedure. (c) Is your result significant at the 5% level? What is your practical conclusion? What is the critical value? If your result is significant at the 5% level, calculate a 95% confidence interval to estimate the value of the parameter p using the same data set. Yes, the result we found is statistically significant at 5%, since < The critical value, is tied to the 5%. The zscore associated with the 5% is (0.5) = The critical value is Sample size needed for an evaluation. You are planning an evaluation of a semesterlong alcohol awareness campaign at your college. Previous evaluations indicate that about 5% of the students surveyed will respond "Yes" to the question "Did the campaign alter your behavior toward alcohol consumption?" How large a sample of students should you take if you want the margin of error for 95% confidence to be about 0.1? * Z The formula is p * (1 p * ) but the issue is what to make p* equal to? Since a previous study m was conducted and the phat value was 5% we could use that as the value of 0.5. (0.5)(0.75) = 73. Another option is to go to the other extreme which would be using 0.5 as 0.1 pstar: (0.5)(0.5) = 97. A last option is to choose a pstar value between 0.5 and 0.5 that we 0.1 would guess is closer to the actual population proportion (parameter) p.
9 8.33 Sample size needed for an evaluation, continued. The evaluation in the previous exercise will also have questions that have not been asked before, so you do not have previous information about the possible value of p. Repeat the calculation above for the following values of p*: 0.1, 0.3, 0.5, 0.7, and 0.9. Summarize the results in a table and graphically. What sample size will you use? 8.34 Are the customers dissatisfied? An automobile manufacturer would like to know what proportion of its customers are dissatisfied with the service received from their local dealer. The customer relations department will survey a random sample of customers and compute a 95% confidence interval for the proportion that are dissatisfied. From past studies, they believe that this proportion will be about Find the sample size needed if the margin of error of the confidence interval is to be no more than 0.0. Using the guessed value: (0.15)(0.85) = Using the conservative (extreme) value: (0.5)(0.5) =
Review for Exam 2. H 0 : p 1 p 2 = 0 H A : p 1 p 2 0
Review for Exam 2 1 Time in the shower The distribution of the amount of time spent in the shower (in minutes) of all Americans is rightskewed with mean of 8 minutes and a standard deviation of 10 minutes.
More informationReview #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
More informationTesting Hypotheses About Proportions
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
More informationOnline 12  Sections 9.1 and 9.2Doug Ensley
Student: Date: Instructor: Doug Ensley Course: MAT117 01 Applied Statistics  Ensley Assignment: Online 12  Sections 9.1 and 9.2 1. Does a Pvalue of 0.001 give strong evidence or not especially strong
More informationMONT 107N Understanding Randomness Solutions For Final Examination May 11, 2010
MONT 07N Understanding Randomness Solutions For Final Examination May, 00 Short Answer (a) (0) How are the EV and SE for the sum of n draws with replacement from a box computed? Solution: The EV is n times
More informationGeneral Method: Difference of Means. 3. Calculate df: either WelchSatterthwaite formula or simpler df = min(n 1, n 2 ) 1.
General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either WelchSatterthwaite formula or simpler df = min(n
More informationHypothesis Testing. Steps for a hypothesis test:
Hypothesis Testing Steps for a hypothesis test: 1. State the claim H 0 and the alternative, H a 2. Choose a significance level or use the given one. 3. Draw the sampling distribution based on the assumption
More informationName: Date: Use the following to answer questions 34:
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
More informationSection 12.2, Lesson 3. What Can Go Wrong in Hypothesis Testing: The Two Types of Errors and Their Probabilities
Today: Section 2.2, Lesson 3: What can go wrong with hypothesis testing Section 2.4: Hypothesis tests for difference in two proportions ANNOUNCEMENTS: No discussion today. Check your grades on eee and
More informationExperimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test
Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely
More informationPower and Sample Size Determination
Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 Power 1 / 31 Experimental Design To this point in the semester,
More informationTerminology. 2 There is no mathematical difference between the errors, however. The bottom line is that we choose one type
Hypothesis Testing 10.2.1 Terminology The null hypothesis H 0 is a nothing hypothesis, whose interpretation could be that nothing has changed, there is no difference, there is nothing special taking place,
More informationReview. March 21, 2011. 155S7.1 2_3 Estimating a Population Proportion. Chapter 7 Estimates and Sample Sizes. Test 2 (Chapters 4, 5, & 6) Results
MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 7 Estimates and Sample Sizes 7 1 Review and Preview 7 2 Estimating a Population Proportion 7 3 Estimating a Population
More informationAP Statistics 2010 Scoring Guidelines
AP Statistics 2010 Scoring Guidelines The College Board The College Board is a notforprofit membership association whose mission is to connect students to college success and opportunity. Founded in
More informationSTAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico. Fall 2013
STAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico Fall 2013 CHAPTER 18 INFERENCE ABOUT A POPULATION MEAN. Conditions for Inference about mean
More informationMargin of Error When Estimating a Population Proportion
Margin of Error When Estimating a Population Proportion Student Outcomes Students use data from a random sample to estimate a population proportion. Students calculate and interpret margin of error in
More informationBUS/ST 350 Exam 3 Spring 2012
BUS/ST 350 Exam 3 Spring 2012 Name Lab Section ID # INSTRUCTIONS: Write your name, lab section #, and ID# above. Note the statement at the bottom of this page that you must sign when you are finished with
More informationSTA 130 (Winter 2016): An Introduction to Statistical Reasoning and Data Science
STA 130 (Winter 2016): An Introduction to Statistical Reasoning and Data Science Mondays 2:10 4:00 (GB 220) and Wednesdays 2:10 4:00 (various) Jeffrey Rosenthal Professor of Statistics, University of Toronto
More informationHypothesis Testing. Bluman Chapter 8
CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 Outline 81 Steps in Traditional Method 82 z Test for a Mean 83 t Test for a Mean 84 z Test for a Proportion 85 2 Test for
More informationThe Math. P (x) = 5! = 1 2 3 4 5 = 120.
The Math Suppose there are n experiments, and the probability that someone gets the right answer on any given experiment is p. So in the first example above, n = 5 and p = 0.2. Let X be the number of correct
More informationModule 5 Hypotheses Tests: Comparing Two Groups
Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this
More informationSTATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS
STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS 1. If two events (both with probability greater than 0) are mutually exclusive, then: A. They also must be independent. B. They also could
More informationSolutions to Homework 6 Statistics 302 Professor Larget
s to Homework 6 Statistics 302 Professor Larget Textbook Exercises 5.29 (Graded for Completeness) What Proportion Have College Degrees? According to the US Census Bureau, about 27.5% of US adults over
More informationThe Normal Approximation to Probability Histograms. Dice: Throw a single die twice. The Probability Histogram: Area = Probability. Where are we going?
The Normal Approximation to Probability Histograms Where are we going? Probability histograms The normal approximation to binomial histograms The normal approximation to probability histograms of sums
More information93.4 Likelihood ratio test. NeymanPearson lemma
93.4 Likelihood ratio test NeymanPearson lemma 91 Hypothesis Testing 91.1 Statistical Hypotheses Statistical hypothesis testing and confidence interval estimation of parameters are the fundamental
More informationChapter 23 Inferences About Means
Chapter 23 Inferences About Means Chapter 23  Inferences About Means 391 Chapter 23 Solutions to Class Examples 1. See Class Example 1. 2. We want to know if the mean battery lifespan exceeds the 300minute
More information3.4 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
More informationUnit 26 Estimation with Confidence Intervals
Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference
More informationChapter 7. Section Introduction to Hypothesis Testing
Section 7.1  Introduction to Hypothesis Testing Chapter 7 Objectives: State a null hypothesis and an alternative hypothesis Identify type I and type II errors and interpret the level of significance Determine
More informationIntroduction to the Practice of Statistics Sixth Edition Moore, McCabe Section 5.1 Homework Answers
Introduction to the Practice of Statistics Sixth Edition Moore, McCabe Section 5.1 Homework Answers 5.18 Attitudes toward drinking and behavior studies. Some of the methods in this section are approximations
More informationHypothesis Tests for 1 sample Proportions
Hypothesis Tests for 1 sample Proportions 1. Hypotheses. Write the null and alternative hypotheses you would use to test each of the following situations. a) A governor is concerned about his "negatives"
More informationChapter 6 Solutions = $0.50. 6.1. σ x = σ/ 25 = $2.50 = 2 $0.50 = $1.00. 6.2. Take two standard deviations: 2 $2.50
Chapter 6 Solutions 6.1. σ x = σ/ 25 = $2.50 5 = $0.50. 6.2. Take two standard deviations: 2 $2.50 5 = 2 $0.50 = $1.00. 6.3. As in the previous solution, take two standard deviations: $1.00. Note: This
More informationAP Statistics 2005 Scoring Guidelines
AP Statistics 2005 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a notforprofit membership association whose mission is to connect students to college
More informationChapter 7 Section 1 Homework Set A
Chapter 7 Section 1 Homework Set A 7.15 Finding the critical value t *. What critical value t * from Table D (use software, go to the web and type t distribution applet) should be used to calculate the
More informationPractice problems for Homework 12  confidence intervals and hypothesis testing. Open the Homework Assignment 12 and solve the problems.
Practice problems for Homework 1  confidence intervals and hypothesis testing. Read sections 10..3 and 10.3 of the text. Solve the practice problems below. Open the Homework Assignment 1 and solve the
More informationIntroduction to the Practice of Statistics Fifth Edition Moore, McCabe
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 5.1 Homework Answers 5.7 In the proofreading setting if Exercise 5.3, what is the smallest number of misses m with P(X m)
More informationMINITAB ASSISTANT WHITE PAPER
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. OneWay
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
STT315 Practice Ch 57 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed
More informationGood luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:
Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours
More informationUniversity of Chicago Graduate School of Business. Business 41000: Business Statistics Solution Key
Name: OUTLINE SOLUTIONS University of Chicago Graduate School of Business Business 41000: Business Statistics Solution Key Special Notes: 1. This is a closedbook exam. You may use an 8 11 piece of paper
More informationCHAPTER 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
More informationMind 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
More informationExtending Hypothesis Testing. pvalues & confidence intervals
Extending Hypothesis Testing pvalues & confidence intervals So far: how to state a question in the form of two hypotheses (null and alternative), how to assess the data, how to answer the question by
More informationChapter 1112 1 Review
Chapter 1112 Review Name 1. In formulating hypotheses for a statistical test of significance, the null hypothesis is often a statement of no effect or no difference. the probability of observing the data
More informationUnit 29 ChiSquare GoodnessofFit Test
Unit 29 ChiSquare GoodnessofFit Test Objectives: To perform the chisquare hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni
More informationUnit 27: Comparing Two Means
Unit 27: Comparing Two Means Prerequisites Students should have experience with onesample tprocedures before they begin this unit. That material is covered in Unit 26, Small Sample Inference for One
More informationHomework 5 Solutions
Math 130 Assignment Chapter 18: 6, 10, 38 Chapter 19: 4, 6, 8, 10, 14, 16, 40 Chapter 20: 2, 4, 9 Chapter 18 Homework 5 Solutions 18.6] M&M s. The candy company claims that 10% of the M&M s it produces
More informationMULTIPLE 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
More informationSTATISTICS 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
More informationMA 1125 Lecture 14  Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.
MA 5 Lecture 4  Expected Values Friday, February 2, 24. Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the
More informationHYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationHYPOTHESIS TESTING WITH SPSS:
HYPOTHESIS TESTING WITH SPSS: A NONSTATISTICIAN S GUIDE & TUTORIAL by Dr. Jim Mirabella SPSS 14.0 screenshots reprinted with permission from SPSS Inc. Published June 2006 Copyright Dr. Jim Mirabella CHAPTER
More informationChapter 14: 16, 9, 12; Chapter 15: 8 Solutions When is it appropriate to use the normal approximation to the binomial distribution?
Chapter 14: 16, 9, 1; Chapter 15: 8 Solutions 141 When is it appropriate to use the normal approximation to the binomial distribution? The usual recommendation is that the approximation is good if np
More informationResults 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 freeresponse questions Question #1: Extracurricular activities
More informationModule 2 Probability and Statistics
Module 2 Probability and Statistics BASIC CONCEPTS Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The standard deviation of a standard normal distribution
More informationChapter 7 Part 2. Hypothesis testing Power
Chapter 7 Part 2 Hypothesis testing Power November 6, 2008 All of the normal curves in this handout are sampling distributions Goal: To understand the process of hypothesis testing and the relationship
More informationMath 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
More informationAn Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10 TWOSAMPLE 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 TWOSAMPLE TESTS Practice
More information** STA 1020  Part 3 (08/Dec/13) ** Exam 3 of 3: Chance and Inference STA 1020 Fall 2013 Section 09 MWF 10:4011:35 0035 State
MATERIAL FOR EXAM #3 Contents Exam 3 of 3: Chance and Inference STA 1020 Fall 2013 Section 09 MWF 10:4011:35 0035 State Instructor: Dr. J.L. Menaldi Textbook  Statistics: Concepts and Controversies,
More informationMULTIPLE 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)
More informationChapter 8 Introduction to Hypothesis Testing
Chapter 8 Student Lecture Notes 81 Chapter 8 Introduction to Hypothesis Testing Fall 26 Fundamentals of Business Statistics 1 Chapter Goals After completing this chapter, you should be able to: Formulate
More informationChapter 8. Hypothesis Testing
Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing
More informationProblem Gambling in New Zealand. Preliminary findings from the New Zealand Health Survey (July 2011 to March 2012)
Problem Gambling in New Zealand Preliminary findings from the New Zealand Health Survey (July 2011 to March 2012) August 2012 Table of contents Summary of key findings... 1 Introduction... 1 Gambling in
More informationFactors affecting online sales
Factors affecting online sales Table of contents Summary... 1 Research questions... 1 The dataset... 2 Descriptive statistics: The exploratory stage... 3 Confidence intervals... 4 Hypothesis tests... 4
More informationStatistical Inference
Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on what would happen if we used this
More informationStatistics 100A Homework 4 Solutions
Chapter 4 Statistics 00A Homework 4 Solutions Ryan Rosario 39. A ball is drawn from an urn containing 3 white and 3 black balls. After the ball is drawn, it is then replaced and another ball is drawn.
More information6.1. Construct and Interpret Binomial Distributions. p Study probability distributions. Goal VOCABULARY. Your Notes.
6.1 Georgia Performance Standard(s) MM3D1 Your Notes Construct and Interpret Binomial Distributions Goal p Study probability distributions. VOCABULARY Random variable Discrete random variable Continuous
More informationInferential Statistics
Inferential Statistics Sampling and the normal distribution Zscores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are
More informationHypothesis Testing I
ypothesis Testing I The testing process:. Assumption about population(s) parameter(s) is made, called null hypothesis, denoted. 2. Then the alternative is chosen (often just a negation of the null hypothesis),
More informationChapter 26: Tests of Significance
Chapter 26: Tests of Significance Procedure: 1. State the null and alternative in words and in terms of a box model. 2. Find the test statistic: z = observed EV. SE 3. Calculate the Pvalue: The area under
More informationsocscimajor yes no TOTAL female 25 35 60 male 30 27 57 TOTAL 55 62 117
Review for Final Stat 10 (1) The table below shows data for a sample of students from UCLA. (a) What percent of the sampled students are male? 57/117 (b) What proportion of sampled students are social
More information2 Precisionbased sample size calculations
Statistics: An introduction to sample size calculations Rosie Cornish. 2006. 1 Introduction One crucial aspect of study design is deciding how big your sample should be. If you increase your sample size
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Sample Practice problems  chapter 121 and 2 proportions for inference  Z Distributions Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide
More informationA POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
CHAPTER 5. A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 5.1 Concepts When a number of animals or plots are exposed to a certain treatment, we usually estimate the effect of the treatment
More informationHow to Conduct a Hypothesis Test
How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some
More informationBasic concepts and introduction to statistical inference
Basic concepts and introduction to statistical inference Anna Helga Jonsdottir Gunnar Stefansson Sigrun Helga Lund University of Iceland (UI) Basic concepts 1 / 19 A review of concepts Basic concepts Confidence
More informationLesson 17: Margin of Error When Estimating a Population Proportion
Margin of Error When Estimating a Population Proportion Classwork In this lesson, you will find and interpret the standard deviation of a simulated distribution for a sample proportion and use this information
More informationCOMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.
277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies
More informationChapter 19 Confidence Intervals for Proportions
Chapter 19 Confidence Intervals for Proportions Use your TI calculator to find the confidence interval. You must know the number of successes, the sample size and confidence level. Under STAT go to TESTS.
More informationPoint and Interval Estimates
Point and Interval Estimates Suppose we want to estimate a parameter, such as p or µ, based on a finite sample of data. There are two main methods: 1. Point estimate: Summarize the sample by a single number
More informationLAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.
More informationOpgaven Onderzoeksmethoden, Onderdeel Statistiek
Opgaven Onderzoeksmethoden, Onderdeel Statistiek 1. What is the measurement scale of the following variables? a Shoe size b Religion c Car brand d Score in a tennis game e Number of work hours per week
More informationSampling and Hypothesis Testing
Population and sample Sampling and Hypothesis Testing Allin Cottrell Population : an entire set of objects or units of observation of one sort or another. Sample : subset of a population. Parameter versus
More informationUnderstanding Confidence Intervals and Hypothesis Testing Using Excel Data Table Simulation
Understanding Confidence Intervals and Hypothesis Testing Using Excel Data Table Simulation Leslie Chandrakantha lchandra@jjay.cuny.edu Department of Mathematics & Computer Science John Jay College of
More informationConfidence Interval: pˆ = E = Indicated decision: < p <
Hypothesis (Significance) Tests About a Proportion Example 1 The standard treatment for a disease works in 0.675 of all patients. A new treatment is proposed. Is it better? (The scientists who created
More informationPastors and Domestic and Sexual Violence Survey of 1,000 Protestant Pastors
Pastors and Domestic and Sexual Violence Survey of 1,000 Protestant Pastors Sponsored by: Sojourners and IMA World Health 2 Methodology The telephone survey of Protestant pastors was conducted May 731,
More informationStat 411/511 THE RANDOMIZATION TEST. Charlotte Wickham. stat511.cwick.co.nz. Oct 16 2015
Stat 411/511 THE RANDOMIZATION TEST Oct 16 2015 Charlotte Wickham stat511.cwick.co.nz Today Review randomization model Conduct randomization test What about CIs? Using a tdistribution as an approximation
More information
An interval estimate (confidence interval) is an interval, or range of values, used to estimate a population parameter. For example 0.476
Lecture #7 Chapter 7: Estimates and sample sizes In this chapter, we will learn an important technique of statistical inference to use sample statistics to estimate the value of an unknown population parameter.
More informationSTAT 350 Practice Final Exam Solution (Spring 2015)
PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects
More informationExecutive summary. Participation in gambling activities (Chapter 2)
Executive summary This report presents results from the British Gambling Prevalence Survey (BGPS) 2010. This is the third nationally representative survey of its kind; previous studies were conducted in
More informationChapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 81 Overview 82 Basics of Hypothesis Testing
Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 81 Overview 82 Basics of Hypothesis Testing 83 Testing a Claim About a Proportion 85 Testing a Claim About a Mean: s Not Known 86 Testing
More informationMath 251, Review Questions for Test 3 Rough Answers
Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,
More informationStats for Strategy Exam 1 InClass Practice Questions DIRECTIONS
Stats for Strategy Exam 1 InClass Practice Questions DIRECTIONS Choose the single best answer for each question. Discuss questions with classmates, TAs and Professor Whitten. Raise your hand to check
More informationChicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011
Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this
More informationModule 7: Hypothesis Testing I Statistics (OA3102)
Module 7: Hypothesis Testing I Statistics (OA3102) Professor Ron Fricker Naval Postgraduate School Monterey, California Reading assignment: WM&S chapter 10.110.5 Revision: 212 1 Goals for this Module
More informationPsychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck!
Psychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck! Name: 1. The basic idea behind hypothesis testing: A. is important only if you want to compare two populations. B. depends on
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More informationHypothesis Testing. Mark Huiskes, LIACS Probability and Statistics, Mark Huiskes, LIACS, Lecture 10
Hypothesis Testing Mark Huiskes, LIACS mark.huiskes@liacs.nl Estimating sample standard deviation Suppose we have a sample x_1,, x_n Average: xbar = (x_1 + + x_n) / n Standard deviation estimate s? Two
More informationNormal Distribution as an Approximation to the Binomial Distribution
Chapter 1 Student Lecture Notes 11 Normal Distribution as an Approximation to the Binomial Distribution : Goals ONE TWO THREE 2 Review Binomial Probability Distribution applies to a discrete random variable
More information5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives
C H 8A P T E R Outline 8 1 Steps in Traditional Method 8 2 z Test for a Mean 8 3 t Test for a Mean 8 4 z Test for a Proportion 8 6 Confidence Intervals and Copyright 2013 The McGraw Hill Companies, Inc.
More information