3. A company which produces tennis balls aims to manufacture tennis balls that have a mean internal pressure of 14 psi, with population standard deviation o = 1.5 psi. In trying to improve efficiency the company alters their manufacturing process slightly. The company knows that this alteration does not change the standard deviation, however, they are unsure if the mean psi has changed. They sample 9 tennis balls produced after this alteration and find that they have the following psi: 12, 13.5, 11, 16, 15, 10, 14, 14.5, 12. Perform a hypothesis test to check whether the mean psi, #, has changed by completing the following steps. (a) State the null and alternative hypotheses. (b) One of the assumptions of hypothesis testing is that the data comes from a normal distribution. Create a normal probability plot using MATLAB. Based on your plot does the assumption of normality seem reasonable? Research Methods and Statistics 2022: Assignment 5 (c) What is our estimate for ? (d) Calculate the standard error. (e) Calculate the 80% confidence interval for /. (f ) Calculate the value of the test statistic. (g) Calculate the p-value. (h) Do you retain or reject the null hypothesis at the 20% level of significance? Provide justification for your answer. (i) What is your conclusion in the context of the problem? (i) Suppose that you have loaded your data into MATLAB with variable name x. What is the command you would use in MATLAB to perform the above calcula- tions? (just give the command, not the output)