Name(s) ECON 2370: Introduction to Economic Data Analysis Due date: Monday, April 4 (Mo-We section) Tuesday, April 5 (Tu-Th sections) PS# Class time: Spring 2016 Homework # 6 1. The following results come from two independent random samples taken of two populations. Sample 1 n1=50 Sample 2 n2=35 x 1=13.6 x 2=11.6 1=2.2 2=3.0 a. What is the point estimate of the difference between the two population means? b. Provide a 90% confidence interval for the difference between the two population means. c. Provide a 95% confidence interval for the difference between the two population means. 1 2. Consumer Reports uses a survey of readers to obtain customer satisfaction ratings for the nation's largest retailers (Consumer Reports, March 2012). Each survey respondent is asked to rate a specified retailer in terms of six factors: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all six factors. Sample data representative of independent samples of Target and Walmart customers are shown below. n1=25 Walmart n2=30 x 1=79 Target x 2=71 a. Formulate the null and alternative hypotheses to test whether there is a difference be- tween the population mean customer satisfaction scores for the two retailers. b. Assume that experience with the Consumer Reports satisfaction rating scale indicates that a population standard deviation of 12 is a reasonable assumption for both retailers. Conduct the hypothesis test and report the p-value. (no need to report the p-value). At a .05 level of significance what is your conclusion? c. Which retailer, if either, appears to have the greater customer satisfaction? d. Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. 2 3. The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514 (College Board website, January 8, 2012). SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. Student's Parents College Grads 485 487 534 533 650 526 554 410 550 515 572 578 497 448 592 469 High School Grads 442 492 580 478 479 425 486 485 528 390 524 535 a. Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. b. What is the point estimate of the difference between the means for the two populations? c. Compute the p-value test statistic for the hypothesis test. d. At = .05, what is your conclusion? 3 4. Bank of America's Consumer Spending Survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment. Using data from a sample of 42 credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). Using the difference data, the sample mean difference was d = $850, and the sample standard deviation was sd = $1123. a. Formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. b. Use a .05 level of significance. Can you conclude that the population means differ? What is the p-value? c. Which category, groceries or dining out, has a higher population mean annual credit card charge? What is the point estimate of the difference between the population means? What is the 95% confidence interval estimate of the difference between the population means? 5. The Professional Golf Association (PGA) measured the putting accuracy of professional golfers playing on the PGA Tour and the best amateur golfers playing in the World 4 Amateur Championship (Golf Magazine, January 2007). A sample of 1075 6-foot putts by professional golfers found 688 made puts. A sample of 1200 6-foot putts by amateur golfers found 696 made putts. a. Estimate the proportion of made 6-foot putts by professional golfers. Estimate the proportion of made 6-foot putts by amateur golfers. Which group had a better putting accuracy? b. What is the point estimate of the difference between the proportions of the two populations? What does this estimate tell you about the percentage of putts made by the two groups of golfers? c. What is the 95% confidence interval for the difference between the two population proportions? Interpret his confidence interval in terms of the percentage of putts made by the two groups of golfers. 5