• Document: Math 3339 Homework 7 (Chapter 9) - Key
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Math 3339 Homework 7 (Chapter 9) - Key Name:__________________________________ PeopleSoft ID:_______________ Instructions: • Homework will NOT be accepted through email or in person. Homework must be submitted through CourseWare BEFORE the deadline. • Print out this file and complete the problems. • Use blue or black ink or a dark pencil. • Write your solutions in the space provided. You must show all work for full credit. • Submit this assignment at http://www.casa.uh.edu under “Assignments" and choose HW7. • Total possible points: 15 1. *Some college students did a study of textbook pricing. They compared pries at the campus bookstore and Amazon.com for the same price. To be fair, they included the sales tax for the local store and the added shipping form Amazon. Here are the prices for a sample of 10 books. Campus Amazon 99.34 113.94 51.53 61.44 20.45 31.59 97.22 108.29 61.89 78.44 58.17 65.74 61.63 63.49 44.63 40.39 96.69 117.99 48.88 58.94 a. We want to determine if there is a significant difference in the price of textbooks from the campus bookstore and from Amazon.com. Which type of test would we use for this data? This is a matched-paired t-test. b. Determine a 95% confidence interval for the difference of the population means. Using R-studio > campus=c(99.34,51.53,20.45,97.22,61.89,58.17,61.63,44.63,96.69,48.88) > amazon=c(113.94,61.44,31.59,108.29,78.44,65.74,63.49,40.39,117.99,58.94) > t.test(campus,amazon,conf.level=.95,paired=T) Paired t-test data: campus and amazon t = -4.372, df = 9, p-value = 0.001792 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -15.146833 -4.817167 sample estimates: mean of the differences -9.982 95% confidence interval: [-15.15, -4.82] c. Interpret your results. Is there a substantial difference between the two ways to be textbook? Assuming that the populations remain unchanged and you have just these two sources, where would you buy? We are 95% confident that the mean of the difference between the cost of the textbook bought from the campus bookstore and amazon is between -$15.15 and -$4.82. It seems that the campus bookstore was less than amazon. ∗ Problems came from Devore, Jay and Berk, Kenneth, Modern Mathematical Statistics with Applications, Thomson Brooks/Cole, 2007. 2. *An article wanted to look at the compression strength of aluminum cans filled with strawberry drink and another sample filled with cola. Does the following data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. What assumptions are necessary for your analysis? Beverage Sample Size Sample Mean Sample SD Strawberry drink 15 540 21 Cola 15 554 15 Let population 1 be the strawberry drink and population 2 be the cola H0: µ1 = µ2 and HA: µ1 < µ2 Test Statistic: 540 − 554 𝑡𝑡 = = −2.101 212 15 2 � + 15 15 p-value = P(t < -2.101) = pt(-2.101,14) = 0.0271 Assuming α = 0.05, p-value < 0.05 we Reject H0 There is strong evidence that the cola cans have a higher average compression strength. Assume that the distribution for both types of cans have a Normal distribution. ∗ Problems came from Devore, Jay and Berk, Kenneth, Modern Mathematical Statistics with Applications, Thomson Brooks/Cole, 2007. 3. Section 9.1 a. Problem 3 b. Problem 4 3. The Payroll data set has data on the numbers of employees and the monthly payroll in thousands of dollars for 50 firms in two different industries. If you divide ”payroll” by ”employees” you get the average monthly salary for each firm. The populations of interest are the firms in industry A and those in industry B. The population variable of interest is the ave

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