# STATS 7 Problems Assignment 2015

1. The Bullet Department Store supplied the following data on customer ages from independent random samples taken at two store locations: Store 1 Store 2 n1 = 36 n2 = 49 x bar1= 40 years x bar2= 35 years s1 = 9 years s2 = 10 yearsFor a .05 level of significance, test the null hypothesis Ho: [µ1 – µ2 = 0] against the alternative hypothesis Ha: [µ1 – µ2 ¹ 0]. What is your conclusion about the mean ages of the populations of customers at the two stores? [15-353]a. Test statistic = -2.41 / critical value = -1.96, so reject the null hypothesisb. Test statistic = 7.04 / critical value = 1.645, so reject the null hypothesisc. Test statistic = 2.41 / critical value = 1.96, so reject the null hypothesisd. Test statistic = -7.04 / critical value = -1.96, so reject the null hypothesise. None of the above answers is correct.2. To estimate if there is a difference between the average daily sales of two branches of a department store, the following data has been gathered: Downtown Store North Mall Store n1 = 12 n2 = 14 x bar1= $36,000 x bar2= $32,000 s1 = $1,200 s2 = $1,000Assuming that the two populations are normally distributed and have equal variances (pooled), with a confidence level of 0.95 (alpha = .05), develop an interval estimate of the difference between the means of the two stores.Hint: Do NOT be bothered if you have to deal with LARGE numbers in your calculations!a. 3094.1356 to 4905.8644b. 3110.0884 to 4889.9116c. 3112.6571 to 4887.3429d. 3568.8413 to 4431.1587e. None of the above answers is correct.3.A random sample of [ cans] of soup produced by Chunky Style provides the weights, measured in ounces in the table below. What is the 95% confidence interval for the standard deviation [s] of the population? Ounces of soup per can12.2 11.9 12.0 12.2 11.7 11.6 11.9 12.0 12.1 12.3 11.8 11.9a. .0222 <= s <= .1274b. .0645 <= s <= .1274c. .0876 <= s <= .1348d. .1348 <= s <= .2174e. None of the above answers is correct.4.The manager of the service department of a local car dealership has noted that the service time of a random sample of [n=15] new automobiles have had a standard deviation of [s=4] minutes. A 95% [a.05] confidence interval estimate for the standard deviation [s] of service times for the population of all their new automobiles isa. 9.46 <= s <= 34.09b. 2.93 <= s <= 6.31c. 3.08 <= s <= 5.84d. 8.58 <= s <= 39.79e. None of the above answers is correct.5. Before the Christmas rush began for the holidays, a department store had noted that the percentage of their customers who use the store's credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers, 46 used the store's credit card; 43 used a major credit card; and 61 paid cash. With alpha = 0.05, test to see if the methods of payment have changed during the Christmas rush. [29?238]a. Test statistic = 5.99 / critical value = 3.72, so reject the null hypothesisb. Test statistic = 5.99 / critical value = 7.81, so do not reject the null hypothesisc. Test statistic = 3.72 / critical value = 2.70, so reject the null hypothesisd. Test statistic = 3.72 / critical value = 5.99, so do not reject the null hypothesise. None of the above answers is correct.6. A lottery is conducted which involves therandom selection of numbers from0 through 4. To make sure that the lottery is fair, arandom sample of [n=250] selections was taken. The following results were obtained: [31-239] Value Frequency 0 40 1 45 2 55 3 60 4 50 ----- 250What is your conclusion about the fairness of the lottery at the 5% level of significance?a. Test statistic = 7.81 / critical value = 3.84, so reject the null hypothesisb. Test statistic = 5.00 / critical value = 9.49, so do not reject the null hypothesisc. Test statistic = 4.94 / critical value = 3.84, so reject the null hypothesisd. Test statistic = 5.00 / critical value = 7.81, so do not reject the null hypothesise. None of the above answers is correct.

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