statistics homework

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timer Asked: Mar 7th, 2018

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please follow the requirement and read carefully the problem 7 set file and do all parts

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ECON 3100 PROBLEM SET 7 Textbook questions: Chapter 13: 3, 5, 11, 15, 19, 25 Statistical investigation: This exercise calls on the data set “analgesics” (a JMP sample data set, available under the “sample data sets” in JMP and on Canvas in the “Data sets” module). The data set contains the following variables: Gender: male or female Drug: which of three drugs was administered, A, B, or C Pain: the patient’s level of pain, with a higher value representing greater pain. 1. Create a table showing the average level of pain for each drug/gender combination. Put “Gender” in the rows of the table and “Drug” in the Columns. What observations can you make about differences in the effectiveness of the three drugs based on your table? 2. Conduct a one-way ANOVA analysis to test whether the average level of pain differs by gender. Be sure to clearly state the null and alternative hypothesis, the test statistic, and the conclusion. . 3. Conduct a one-way ANOVA analysis to test whether the average level of pain differs by the drug taken. Be sure to clearly state the null and alternative hypothesis, the test statistics, and the conclusion. . 4. Summarize your findings accurately and concisely in a brief paragraph. Everyday Statistics This question is based on the article “The Myth, the Math, the Sex,” which follows this question. Suppose that you were conducting statistical research, using ANOVA to test for a difference in the average number of sexual partners reported by men and the number reported by women. 1. What would be the response (dependent) variable in the study? 2. What would be the “treatment” or “factor” in the study? 3. What would be the null hypothesis? 4. Based on the information in the article and men’s and women’s survey responses, what would you expect the conclusion to be? 5. Near the end of the article, Dr. Gale states, “the false conclusions people draw from these surveys may have a sort of self-fulfilling prophecy.” Why must the conclusions people draw from these surveys be false? 6. In your opinion, are people influenced by survey results- that is, do people shape their behavior to match what survey results claim to be “normal” (or the opposite-do they try to stand out from the norm)? 1 August 12, 2007 IDEAS & TRENDS The Myth, the Math, the Sex By GINA KOLATA EVERYONE knows men are promiscuous by nature. It’s part of the genetic strategy that evolved to help men spread their genes far and wide. The strategy is different for a woman, who has to go through so much just to have a baby and then nurture it. She is genetically programmed to want just one man who will stick with her and help raise their children. Surveys bear this out. In study after study and in country after country, men report more, often many more, sexual partners than women. One survey, recently reported by the federal government, concluded that men had a median of seven female sex partners. Women had a median of four male sex partners. Another study, by British researchers, stated that men had 12.7 heterosexual partners in their lifetimes and women had 6.5. But there is just one problem, mathematicians say. It is logically impossible for heterosexual men to have more partners on average than heterosexual women. Those survey results cannot be correct. It is about time for mathematicians to set the record straight, said David Gale, an emeritus professor of mathematics at the University of California, Berkeley. “Surveys and studies to the contrary notwithstanding, the conclusion that men have substantially more sex partners than women is not and cannot be true for purely logical reasons,” Dr. Gale said. He even provided a proof, writing in an e-mail message: “By way of dramatization, we change the context slightly and will prove what will be called the High School Prom Theorem. We suppose that on the day after the prom, each girl is asked to give the number of boys she danced with. These numbers are then added up giving a number G. The same information is then obtained from the boys, giving a number B. Theorem: G=B 2 Proof: Both G and B are equal to C, the number of couples who danced together at the prom. Q.E.D.” Sex survey researchers say they know that Dr. Gale is correct. Men and women in a population must have roughly equal numbers of partners. So, when men report many more than women, what is going on and what is to be believed? “I have heard this question before,” said Cheryl D. Fryar, a health statistician at the National Center for Health Statistics and a lead author of the new federal report, “Drug Use and Sexual Behaviors Reported by Adults: United States, 1999-2002,” which found that men had a median of seven partners and women four. But when it comes to an explanation, she added, “I have no idea.” “This is what is reported,” Ms. Fryar said. “The reason why they report it I do not know.” Sevgi O. Aral, who is associate director for science in the division of sexually transmitted disease prevention at the Centers for Disease Control and Prevention, said there are several possible explanations and all are probably operating. One is that men are going outside the population to find partners, to prostitutes, for example, who are not part of the survey, or are having sex when they travel to other countries. Another, of course, is that men exaggerate the number of partners they have and women underestimate. Dr. Aral said she cannot determine what the true number of sex partners is for men and women, but, she added, “I would say that men have more partners on average but the difference is not as big as it seems in the numbers we are looking at.” Dr. Gale is still troubled. He said invoking women who are outside the survey population cannot begin to explain a difference of 75 percent in the number of partners, as occurred in the study saying men had seven partners and women four. Something like a prostitute effect, he said, “would be negligible.” The most likely explanation, by far, is that the numbers cannot be trusted. 3 Ronald Graham, a professor of mathematics and computer science at the University of California, San Diego, agreed with Dr. Gale. After all, on average, men would have to have three more partners than women, raising the question of where all those extra partners might be. “Some might be imaginary,” Dr. Graham said. “Maybe two are in the man’s mind and one really exists.” Dr. Gale added that he is not just being querulous when he raises the question of logical impossibility. The problem, he said, is that when such data are published, with no asterisk next to them saying they can’t be true, they just “reinforce the stereotypes of promiscuous males and chaste females.” In fact, he added, the survey data themselves may be part of the problem. If asked, a man, believing that he should have a lot of partners, may feel compelled to exaggerate, and a woman, believing that she should have few partners, may minimize her past. “In this way,” Dr. Gale said, “the false conclusions people draw from these surveys may have a sort of self-fulfilling prophecy.” 4 Textbook questions: Chapter 13: 3, 5, 11, 15, 19, 25 3. Use the F table to determine the value beyond which you would find a. 1% of the values, if numerator degrees of freedom = 3 and denominator degrees of freedom = 13. b. 5% of the values, if numerator degrees of freedom = 2 and denominator degrees of freedom = 20. c. 1% of the values, if numerator degrees of freedom = 3 and denominator degrees of freedom = 17. 5. Use a statistical calculator or Excel's F.DIST.RT function to determine the proportion of values in an F distribution that are greater than 1. 3.285, if numerator degrees of freedom = 4 and denominator degrees of freedom = 18. 2. 5.701, if numerator degrees of freedom = 1 and denominator degrees of freedom = 12. 3. 7.238, if numerator degrees of freedom = 5 and denominator degrees of freedom = 28. 11. As sales reps for Nguyen Products, Byron and Anita have generally produced the same average weekly sales volume, but the “consistency” (as measured by the variance of weekly sales) of the two sales reps appears to be different. You take independent random samples of six weeks of sales for each of the two reps. Results (in $1000s) are shown below. 1. Test the null hypothesis that the two populations represented here have equal variances. Assume that both population distributions are normal. Use a significance level of 10%. 2. Can you make the case from this sample data that Byron's sales are less consistent (have a larger variance) than Anita's? That is, can we reject a null hypothesis that the variance of Byron's sales is no greater than the variance of Anita's sales? Use a significance level of 5%. 15. You have conducted recent tests measuring peak pollution levels in various parts of the city. The average peak pollution readings for a sample of 21 days at each of three city locations are given in the table below, along with sample standard deviations. Test the hypothesis that the average peak pollution levels for the three populations represented here are the same. Use a significance level of 5%. 19. Goveia Inc. is evaluating three possible bonus incentive programs for its sales staff. During a trial period lasting four months, five sales staff members were randomly assigned to each bonus program. Individual sales figures (in $millions) are shown below: 1. Test the hypothesis that average sales for the three populations represented here are the same. Use a significance level of 5%. (Use Expression 13.2 to compute the within-groups sum of squares (SSW) for your analysis.) 2. Show the proper ANOVA table summarizing your work in part a. 25. Elam Industries is interested in assessing customer response to four possible national promotional campaigns. Twenty retail stores were randomly selected for a preliminary trial. The twenty stores were randomly divided into four groups of five stores and each group was randomly assigned a different promotion. At the end of the trial period, average response rates were calculated for each of the four groups. Complete the ANOVA table below and use the information in the table to test a null hypothesis that the average response rate would be the same for the four populations represented in the trial. Use a significance level of .05. Report your conclusion and explain your reasoning. Textbook questions: Chapter 13: 3, 5, 11, 15, 19, 25 3. Use the F table to determine the value beyond which you would find a. 1% of the values, if numerator degrees of freedom = 3 and denominator degrees of freedom = 13. b. 5% of the values, if numerator degrees of freedom = 2 and denominator degrees of freedom = 20. c. 1% of the values, if numerator degrees of freedom = 3 and denominator degrees of freedom = 17. 5. Use a statistical calculator or Excel's F.DIST.RT function to determine the proportion of values in an F distribution that are greater than 1. 3.285, if numerator degrees of freedom = 4 and denominator degrees of freedom = 18. 2. 5.701, if numerator degrees of freedom = 1 and denominator degrees of freedom = 12. 3. 7.238, if numerator degrees of freedom = 5 and denominator degrees of freedom = 28. 11. As sales reps for Nguyen Products, Byron and Anita have generally produced the same average weekly sales volume, but the “consistency” (as measured by the variance of weekly sales) of the two sales reps appears to be different. You take independent random samples of six weeks of sales for each of the two reps. Results (in $1000s) are shown below. 1. Test the null hypothesis that the two populations represented here have equal variances. Assume that both population distributions are normal. Use a significance level of 10%. 2. Can you make the case from this sample data that Byron's sales are less consistent (have a larger variance) than Anita's? That is, can we reject a null hypothesis that the variance of Byron's sales is no greater than the variance of Anita's sales? Use a significance level of 5%. 15. You have conducted recent tests measuring peak pollution levels in various parts of the city. The average peak pollution readings for a sample of 21 days at each of three city locations are given in the table below, along with sample standard deviations. Test the hypothesis that the average peak pollution levels for the three populations represented here are the same. Use a significance level of 5%. 19. Goveia Inc. is evaluating three possible bonus incentive programs for its sales staff. During a trial period lasting four months, five sales staff members were randomly assigned to each bonus program. Individual sales figures (in $millions) are shown below: 1. Test the hypothesis that average sales for the three populations represented here are the same. Use a significance level of 5%. (Use Expression 13.2 to compute the within-groups sum of squares (SSW) for your analysis.) 2. Show the proper ANOVA table summarizing your work in part a. 25. Elam Industries is interested in assessing customer response to four possible national promotional campaigns. Twenty retail stores were randomly selected for a preliminary trial. The twenty stores were randomly divided into four groups of five stores and each group was randomly assigned a different promotion. At the end of the trial period, average response rates were calculated for each of the four groups. Complete the ANOVA table below and use the information in the table to test a null hypothesis that the average response rate would be the same for the four populations represented in the trial. Use a significance level of .05. Report your conclusion and explain your reasoning. S S SS. S S S S D'R 07 M a Nev 09 х a G G Nev o х * -6X со - Secure https://desktop.seattleu.edu/portal/webclient/index.html#/desktop Analgesics - JMP Pro File Edit Tables Rows Cols Analyze Graph Tools View Window Help * ED ED HAM Analgesics > Notes Example of factorial experime gender drug pain Fit Model 1 male C 12 2 female A 8 3 male C 14 4 female A 10 5 male C 12 6 female А 9 7 female A 7 8 female A 2 Columns (370) 9 female A 7 gender 10 female A 6 drug 11 male B 13 pain 12 female C 12 13 female A 7 14 male C 14 15 male A 8 16 male B 17 17 female с 9 18 male C Rows 11 33 19 female B 8 Selected 1 20 male А 7 Excluded 0 21 female A 7 Hidden 0 22 male B 10 Labelled 0 23 female A 7 All rows Start X W A 12:34 AM 3/7/2018 HI W Problem Set 7-1.doc W 20180306070810p...doc ^ 20180302084035n....pdf 20180227232810....docx A W 20180227225353....docx A Show all х 1 O Type here to search Q E e w x] 60 Ma cx 12:34 AM 3/7/2018 民 S S SS. S S S S D'R 07 M a Nev 09 х a G G Nev o х * { со Secure https://desktop.seattleu.edu/portal/webclient/index.html#/desktop Analgesics - JMP Pro File Edit Tables Rows Cols Analyze Graph Tools View Window Help HA EN - 6X Analgesics > Notes Example of factorial experime Fit Model drug pain gender 12 female 13 female C 12 A 7 14 male 14 15 male C A B 8 17 9 16 male 17 female 18 male 19 female 20 male 21 female 22 male C C B 11 A Columns (370) gender drug pain 8 7 7 A 10 23 female B A A 7 7 A 7 C 2 B B 8 4 24 female 25 female 26 female 27 male 28 female 29 male 30 male 31 male 32 female 33 male B 9 Rows All rows A A 331 0 0 0 0 Selected Excluded Hidden Labelled 7 7 5 8 A д Start X W A 12:35 AM 3/7/2018 W Problem Set 7-1.doc W 20180306070810p...doc ^ 20180302084035n....pdf 20180227232810....docx A W 20180227225353....docx A Show all х 1 O Type here to search Q E e w x] 60 a 4x 12:35 AM 3/7/2018
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