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CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 7.8 minutes. A sample of actual waiting times will be used to test this assumption and determine whether actual mean waiting time differs from this standard. a. Formulate the hypotheses for this application. Ho : H = 7.8 Ha : M # 7.8 b. A sample of 140 shoppers showed a sample mean waiting time of 8.7 minutes. Assume a population standard deviation of o = 3.2 minutes. What is the p-value? z value * (to 2 decimals) p-value X (to 4 decimals) C. At a = 0.05, what is your conclusion? Reject null hypothesis Can conclude that the population mean waiting time differs from 7.8 minutes. d. Compute a 95% confidence interval for the population mean. Does it support your conclusion? x )(to 2 decimals) No v O; u = 7.8 is not in the interval .Consider the following hypothesis test: H a: p. = 1? H a: p. g 1? A sample of 50 provided a sample mean of 14.36. The population standard deviation is 4. u u a. Compute the value ofthe test statistic (to 2 decimals). (If answer is negative. use minus sign.) 0 b. what is the pvalue (to 4 decimals]? 0 c. Using a = .05, can it be concluded that the population mean is not equal to 1?? 9 Answer the next three questions using the critical value approach. d. Using a = .05, what are the critical values for the test statistic [to 2 decimals)? a: 0 a. State the rejection rule: Reject H o if: is 9 the lower critical value and is 9 the upper critical value. I. Can it be concluded that the population mean is not equal to 1?? - Wall Street securities firms paid out record year-end bonuses of $125,500 per employee for 2005 (Fortune, February 6, 2006). Suppose we would like to take a sample of employees at the Jones & Ryan securities firm to see whether the mean year-end bonus is different from the reported mean of $125,500 for the population. a. State the null and alternative hypotheses you would use to test whether the year-end bonuses paid by Jones & Ryan were different from the population mean. Ho: / equal to 125,500 Ha: / not equal to 125,500 b. Suppose a sample of 40 Jones & Ryan employees showed a sample mean year-end bonus of $118,000. Assume a population standard deviation of $31,000 and compute the p-value (to 4 decimals). 0.1665 c. With a = .05 as the level of significance, what is your conclusion? Do not conclude that the year-end bonuses paid by Jones & Ryan were different from the population mean Answer the next three questions using the critical value approach. d. Using a = .05, what is the critical value for the test statistic? +/- 1.96 0 e. Calculate the test statistic (to 2 decimals). -1.38 *