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The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of 14 minutes before being able to talk to an IRS employee. Suppose you select a sample of 50 callers after the new phone service has been implemented; the sample results show a mean waiting time of 12 minutes before an IRS employee comes on line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting times is 10 minutes. Use =0.05. a. State the hypotheses. H0: Ha: b. What is the p-value (to 4 decimals)? c. Using =0.05, can you conclude that the actual mean waiting time is significantly less than the claim of 14 minutes made by the taxpayer advocate. At Western University the historical mean of scholarship examination scores for freshman applications is 900 . A historical population standard deviation =180 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed. a. State the hypotheses. H0: H: b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean 935 (to the nearest whole number)? c. Use the confidence interval to conduct a hypothesis test. Using =0.05, can the assistant dean conclude that the mean examination score for the new freshman applications has changed? d. What is the p-value (to 3 decimals)