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Solve This Problem

Problem 1: The weekly salary of all customer service workers of a company has had mean of $400 with standard deviation $48.6. In contract negotiation, the company claims that a new incentive scheme has increased the average weekly earnings for all workers. A union representation takes a random sample of 15 workers and finds that their weekly earning have an average of $421.35.

(a) Test the company claims at 5% level of significance. Sketch the distribution of test statistic under null and alternative hypothesis showing rejection region.

(b) Find 95% CI for the population mean of weekly salary and P-values. Based on CI and P-value, would you able to have same conclusion that obtained in (a)?

Problem2 : The past records of a supermarket show that its customers spend an average of $95 per visit at this store. Recently the management of the store initiated a promotional campaign according to which each customer receives points based on the total money spent at the store, and these points can be used to buy products at the store. The management expects that as a result of this campaign, the customers should be encouraged to spend more money at the store. To check whether this is true, the manager of the store took a sample of 14 customers who visited the store. The following data give the money (in dollars) spent by these customers at this supermarket during their visits.

109 136 107 116 101 109 110 94 101 97 104 83 67 120

Assume that the money spent by all customers at this supermarket has a normal distribution. Using a 5% significance level, can you conclude that the mean amount of money spent by all customers at this supermarket after the campaign was started is more than $95?

Problem 3: According to the analysis of Federal Reserve statistics and other government data, American households with credit card debts owed an average of $15,706 on their credit cards in August 2015 (www.nerdwallet.com). A recent random sample of 500 American households with credit card debts produced a mean credit card debt of $16,377 with a standard deviation of $3800. Do these data provide significant evidence at a 1% significance level to conclude that the current mean credit card debt of American households with credit card debts is higher than $15,706? Use both the p-value approach and the critical-value approach.

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