need these three problems answered, 

4. The director of admissions at Long Beach Hospital believes that patient residence time (i.e., the length of stay in the hospital) has been dropping over the last several years. Two years ago the average residence time was four days. The director examines the records of 40 recently released patients and finds that the average residence time was 3.5 days with a standard deviation of 1.2 days. What conclusions regarding patient residence time can be drawn from the survey results at a 90% level of confidence? As part of your assessment, include a statement of the null and alternate hypothesis, decision criteria, test statistic, decision, and the p -value.

8. A survey was conducted to assess whether middle-income wages have changed recently from the historic average of $85,000. A random sample of 25 incomes was obtained, and showed a mean of $85,900 with a standard deviation of $1,350. Does the survey indicate a significant change has occurred, at the 0.01 level? As part of your assessment, include a statement of the null and alternate hypothesis, decision criteria, test statistic, decision, and the p-value.

10. A call center is monitoring its wait times, to ensure they remain less than 5 minutes, with a standard deviation of 2 minutes. A recent sample of 100 calls shows the mean wait time is 4.8 minutes. Can the call center continue to claim that wait times are less than 5 minutes, at a 0.10 level of significance? As part of your assessment, include a statement of the null and alternate hypothesis, decision criteria, test statistic, decision, and the p-value.