Question 8 [10 marks] A pressure-relief valve (PRV) is installed on a residential hot-water heater to protect against overheating and, of course, high pressure. Independent random samples of PRVs from different companies were obtained. Each value was tested by recording the pressure (in pounds per square inch, psi) required to cause the valve to open. The summary statistics are given in the table. size mean variance Assume the underlying populations are normal, with unequal variances. a. [7 marks] Is there any evidence to suggest that the mean pressure required to open each valve is different? Use the level of signicance a=0.05. i. [3 marks] Let company Delta be population 11 and company Gamma be population 2. State the four parts of the hypothesis test. ii. [2 marks] Determine the value of the test statistic. iii. [2 marks] Is there any evidence to suggest that the mean pressure required to open each valve is different? b. [3 marks] Find a 95% confidence interval for the difference in population mean pressure required to open each valve. Is this condence interval consistent with the results in part (a)? Explain your