1 COURSE: DSCI 3710 Print Name: Exam 1 Signature: Maymester 2011 Student ID#: INSTRUCTIONS: - Please print your name and student ID number on this exam. Also, put your signature on this exam. - On your scantron PRINT your name and exam version. - You have 120 minutes to complete this exam. The exam is open book, open notes, and open mind. You may use any type of hand calculator but please show all your work on the exam and mark all answers on the scantron. Usage of cell phones, digital cameras, PDAs, and other communication devices is prohibited. - Please DO NOT pull this exam apart. When you have completed the exam, please turn your scantron and exam booklet into your instructor, at the front desk. - Good luck and we wish you well on the exam. Note: Whenever question(s) are connected you may be asked to assume a result (given a value) as an answer for the previous question but this result (value) may or may not be correct. The procedure is set in place to prevent you from losing points on a subsequent question because you made a mistake on some previous question/s. 2 Use the information given in the next paragraph to answer the next three questions. An accountant for Dan’s pizza franchise claims that stores in their franchise, which generate an average of monthly revenue of $57,000 per store, are doing worse than the market average across all remaining pizza franchises. She hires a consultant and obtains a sample of revenues from 23 stores belonging to various different franchises and finds that the average monthly revenue per store is $58,000. She conducts a statistical analysis on the data using Excel, the results of which are shown below at the 0.01 significance level. t Test for Population Mean Dan's Pizza Number of Observations 23 Sample Standard Deviation 5567.66 Sample Mean 58000 Ho: XXXX Ha: XXXX T* 0.861373 P[T >T*] 0.199162 T Critical, = 0.01 2.50832 1. Which of the following would be appropriate for the null hypothesis? A. μ > 57000 B. μ < 57000 C. μ = 57000 D. μ < 57000 E. μ > 57000 2. The decision rule, based on a table value and 1% significance level, is reject Ho if the calculated value is A. > 0.199 B. > 0.861 C. < 1.717 D. < 2.074 E. > 2.508 3. Based upon the output shown above, what is the conclusion of the hypothesis test? A. Conclude there is evidence Dan’s pizza franchise is performing worse than the market average because the p-value is greater than the significance level. B. Conclude there is evidence Dan’s pizza franchise is performing worse than the market average because the p-value is smaller than the significance level. C. Conclude there is insufficient evidence Dan’s pizza franchise is performing worse than the market average because the p-value is greater than the significance level. D. Conclude there is insufficient evidence Dan’s pizza franchise is performing worse than the market average because the p-value is smaller than the significance level. E. Conclude there is evidence Dan’s pizza franchise is performing worse than the market average because the test statistic is greater than the significance level. 3 Use the information given in the next paragraph to answer the next three questions. A recent commercial claims that the international phone call rates offered by IDT are lower than those of MCI. A consumer decided to test this claim by collecting and analyzing data from IDT’s and MCI’s Web sites (www.idt.net, www.mci.com). The statistical analysis of rates offered by each company, in cents per minute, for international calls from the U.S. to 14 selected countries is listed below. t-Test: Paired Two Sample for Means, = 0.05 MCI IDT Mean 15.21429 15.95Variance 46.95055 186.12731Observations 14 14Pearson Correlation 0.867511 Hypothesized Mean Difference 0 df xxxxxx t Stat -0.32696 P(T<=t) one-tail 0.374452 t Critical one-tail 1.770932 P(T<=t) two-tail 0.748903 t Critical two-tail 2.160368 4. What is the table value (at the 5 % level) of the appropriate test statistic to test the belief that IDT rates are lower? A. 1.77 B. 0.374 C. 0.748 D. 2.160 E. 0.867 5. What is the absolute point estimate of difference in international phone call rates? A. 1 B. 0.74 C. 0.867 D. 14 E. 13 6. Based upon the output shown above, what is the conclusion of the hypothesis test, to test the belief that IDT rates are lower? A. Reject the null hypothesis, conclude that IDT rates are lower B. Reject the null hypothesis, conclude that IDT rates are not lower C. Fail to reject the null hypothesis, conclude that IDT rates are not lower D. Fail to reject the null hypothesis, conclude that IDT rates are lower E. Fail to reject the null hypothesis, conclude that IDT rates are the same and MCI 4 Use the information given below to answer the next five questions. The CEO of Mean Green Cab Company believes there is a difference between the durability of two brands of tires, BillW and KellyH. The CEO decides to test her belief by running an experiment. To conduct the experiment, her R & D department uses a machine with a metallic device to wear down the tires and records the tread depth on tires of each brand after new tires are spun for an equivalent of 10,000 miles. A random sample of 12 tires each of brand BillW and brand KellyH were tested. Do the results displayed in the Excel output below support the claim that there is a difference between the durability of two brands of tires, BillW and KellyH? A significance level of α = 0.01 was used for the test. Assume that the population variances are equal and that the two populations are normally distributed. t-Test: Two-Sample Assuming Equal Variances BillW KellyH Mean 130.583 105.5Variance 894.083 920.272Observations 12 12Pooled Variance xxxxxxHypothesized Mean Difference 0df 22t Stat 2.0399P(T<=t) one-tail 0.0267t Critical one-tail xxxxxxP(T<=t) two-tail 0.0535t Critical two-tail xxxxxx 7. To test the claim that there is a difference between the durability of BillW and KellyH brands (μB – μK), which of the following is the (absolute) critical value of the test statistic at the 1% level of significance? A. 2.82 B. 2.51 C. 2.57 D. 2.33 E. 2.65 8. The calculated value of the test
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