COMM207 Business Statistics II Assignment I Fall 2016 COMM 207 - Assignment I Due date: October 6, 2016 (at the beginning of class) 1. The Black Fly Beverage Company has just installed a new bottling process that will fill 500-mL bottles of its popular margarita beverage. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company a considerable amount of money. To verify that the filler is set up correctly, the company wants to see whether the mean bottle fill, , is close to the target fill of 500 mL. To this end, a random sample of 36 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that the mean bottle fill is the desired 500 mL, the filler's initial setup will be readjusted. a. The bottling company wants to set up a hypothesis test so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hypotheses for this hypothesis test. b. In the context of this situation, interpret making a Type I error; interpret making a Type II error. 2. National Motors has equipped the ZX-900 with a new disc brake system. We define m to be the mean stopping distance (from a speed of 55 km/h) of all ZX-900s. National Motors would like to claim that the ZX-900 achieves a shorter mean stopping distance than the 20 metres claimed by a competitor. a. Set up the null and alternative hypotheses needed to support National Motors' claim. b. A television network will allow National Motors to advertise its claim if the appropriate null hypothesis can be rejected at = .05. If a random sample of 81 ZX-900s have a mean stopping distance of 19.27 metres, will National Motors be allowed to advertise the claim? Assume that = 2 m and justify your answer using both a critical value and a pvalue. 3. A group of researchers presented 205 research participants (all of whom were marketing researchers) with a series of scenarios involving ethical issues such as confidentiality, conflict of interest, and social acceptability. One of the scenarios presented to the participants was as follows: A marketing testing firm to which X Company gives most of its business recently went public. The marketing research director of X Company had been looking for a good investment and proceeded to buy some $20,000 of their stock. The firm continues as X Company's leading supplier for testing. Of the 205 marketing researchers who participated in the ethics survey, 111 said that they disapproved of the actions taken in the scenario. a. Let p be the proportion of all marketing researchers who disapprove of the actions taken in the conflict of interest scenario. Set up the null and alternative hypotheses COMM207 Business Statistics II Assignment I Fall 2016 needed to attempt to provide evidence supporting the claim that a majority of all marketing researchers disapprove of the actions taken. b. Assuming that the sample of 205 marketing researchers has been randomly selected, use critical values and the previously given sample information to test the hypotheses you set up in part (a) at the .10, .05, .01, and .001 levels of significance. How much evidence is there that a majority of all marketing researchers disapprove of the actions taken? c. Suppose a random sample of 1,000 marketing researchers reveals that 540 of the researchers disapprove of the actions taken in the conflict of interest scenario. Use critical values to determine how much evidence there is that a majority of all marketing researchers disapprove of the actions taken. d. Note that in parts (b) and (c) the sample proportion is essentially the same. Explain why the results of the hypothesis tests in parts (b) and (c) differ. 4. In the Journal of Marketing, Bayus studied differences between \"early replacement buyers\" and \"late replacement buyers.\" Suppose that a random sample of 800 early replacement buyers yields a mean number of dealers visited of , and that a random sample of 500 late replacement buyers yields a mean number of dealers visited of . Assuming that the standard deviation for early replacement buyers is .66, and the standard deviation for late replacement buyers is .71, and assuming that the samples are independent: a. Set up the null and alternative hypotheses needed to attempt to show that the mean number of dealers visited by late replacement buyers exceeds the mean number of dealers visited by early replacement buyers by more than 1. b. Test the hypotheses you set up in part (a) by using critical values and by setting equal to .10, .05, .01, and .001. How much evidence is there that H0 should be rejected? c. Find the p-value for testing the hypotheses you set up in part (a). Use the p-value to test these hypotheses with a equal to .10, .05, .01, and .001. How much evidence is there that H0 should be rejected? Explain your conclusion in practical terms. d. Do you think that the results of the hypothesis tests in parts (b) and (c) have practical significance? Explain and justify your answer. 5. In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss evaluating the effectiveness of a test coupon. Samples of 500 test coupons and 500 control coupons were randomly delivered to shoppers. The results indicated that 35 of the 500 control coupons were redeemed, while 50 of the 500 test coupons were redeemed. COMM207 Business Statistics II Assignment I Fall 2016 a. In order to consider the test coupon for use, the marketing research organization required that the proportion of all shoppers who would redeem the test coupon be statistically shown to be greater than the proportion of all shoppers who would redeem the control coupon. Assuming that the two samples of shoppers are independent, carry out a hypothesis test at the .01 level of significance that will show whether this requirement is met by the test coupon. Explain your conclusion. b. Carry out the test of part (a) at the .10 level of significance. What do you conclude? Is your result statistically significant? 6. Let p1 represent the population proportion of Canadian women who are in favour of a new modest tax on "junk food". Let p2 represent the population proportion of Canadian men who are in favour of a new modest tax on "junk food". Out of the 265 women surveyed, 106 of them are in favour of a "junk food" tax. Out of the 285 men surveyed, only 57 of them are in favour a "junk food" tax. At = 0.01, can we conclude that the proportion of women who favour "junk food" tax is more than 5% higher than proportion of men who favour the new tax? 7. A marketing research company surveyed grocery shoppers in the east and west coasts to see the percentage of the customers who prefer chicken to other meat. The data are given below. Is the proportion of customers who prefer chicken higher at the West Coast? Test at 0.05 significant level. 8. Consider a chemical company that wants to determine whether a new catalyst, Catalyst XA-100, changes the mean hourly yield of its chemical process from the historical process mean of 750 kilograms per hour. When five trial runs are made using the new catalyst, the following yields (in kilograms per hour) are recorded: 801, 814, 784, 836, and 820. a. Letting be the mean of all possible yields using the new catalyst, set up the null and alternative hypotheses needed if we want to attempt to provide evidence that differs from 750 kilograms. b. The mean and the standard deviation of the sample of five catalyst yields are and s = 19.647. Using a critical value and assuming approximate normality, test the hypotheses you set up in part (a) by setting equal to .01. The p-value for the hypothesis test is given in the Excel output on the page margin. Interpret this p-value. Present a standardized effect size estimate to accompany the hypothesis test. COMM207 Business Statistics II Assignment I Fall 2016 9. Given sample data: .612, .619, .628, .631, .640, .643, .649, .655, .663, and .679, test H0: .625 versus HA: > .625 at alpha =.10. Assume the population is normally distributed. 10. Test H0: 1 2, HA: 1 > 2 at = .10, where 1 = 77.4, 2 = 72.2, s1 = 3.3, s2 = 2.1, n1 = 6, n2 = 6. Assume equal population variances, normally distributed populations, and independent random samples. 11. Suppose a sample of 11 paired differences that has been randomly selected from a normally distributed population of paired differences yields a sample mean of and a sample standard deviation of sd = 5. a. Test the null hypothesis H0: d 100 versus H: d > 100 by setting alpha equal to .05 and .01. How much evidence is there that d = 1 2 exceeds 100? b. Test the null hypothesis H0: d 110 versus H: d < 110 by setting alpha equal to .05 and .01. How much evidence is there that d = 1 2 is less than 110? 12. A marketing manager wants to compare the mean prices charged for two brands of CD players. The manager conducts a random survey of retail outlets and obtains independent random samples of prices with the following results: (assume normality) Use the sample information to test H0: 12 = 22 versus H: 12 22 with = .05. Based on this test, does it make sense to use the equal variances procedure? Explain. 13. Test H0: 12 22, HA: 12 > 22 at alpha = .05 where n1 = 16, n2 = 19, s12 = .03, s22 = .02