1.. Mountain States Surgery Center in Denver, Colorado, performs many knee-replacement procedures each year.Research physicians at Mountain States have developed a surgery procedure they believe will reduce the average patient recovery time.The hospital board will not recommend the new procedure unless there is substantial evidence to suggest that it is better than the existing procedure.Records indicate that the current mean recovery time for the existing procedure is 142 days.

To test whether the new procedure actually results in a lower mean recovery time, the new procedure was performed on a random sample of 36 patients.

Let be the recovery time of all knee replacement patients.The null hypothesis is that the mean recovery time for all knee replacement patients is at least 142 days.

The sample of 36 patients had an average recovery time of 138.5 days and a sample standard deviation of 20.What is the value of the test statistic?Include 2 decimal places in your answer.

2.. The owner of a local nightclub has recently surveyed a random sample of n = 50 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Her null and alternative hypotheses are:

H₀: 30

H_A: >30.

The calculated value of her test statistic is 2.38.What is the p-value?Include 4 decimal places in your answer.

3..In a sample of size n=16 from a normal distribution,=53 and s=20.You are testing the null hypothesis H₀: =50?

The value of t_c is 0.60.What is the p-Value of this test statistic?Include 4 decimal places in your answer.