For part a, I tried the difference between two means test for part a, but the answer seems wrong. I have no idea where to start for any of these parts. Can you help?

2. An airline passenger's value of time (VOT) is measured as the amount of money a passenger is willing to pay to avoid being delayed by an additional minute. A passenger is classied as either a business- passenger or as a leisure-passenger based on the purpose of travel. Economic theory suggests that the value of time should be higher for business-passengers than for the leisure-passengers, in general. It is well-known from prior studies on the variability in the passengers' socio-economic statuses that the standard deviation in VOT for business-passengers is approximately 0.25 S/min and for leisure- passengers, it is approximately 0.15 S/min. Using the results from a survey of US domestic airline passengers involving a sample of 50 business-passengers and 50 leisure-passengers, you tested the null hypothesis that the mean VOT for business-passengers (,ub) is less than or equal to that for the leisure-passengers (,ug), i.e., Ho: ,ub S it; against the appropriate alternate hypothesis. Assume that, in fact, the true difference is ,ub m = 0.1, and use this as the specific alternate hypothesis. a. What is the power of the hypothesis test made at the 5% significance level? b. If we decide to increase the survey sample size for the business-passengers (owing to their greater variance in VOT) while keeping the sample size of the leisure-passengers constant, then what is the minimum sample size for the business-passengers that is needed to have a power of 95% for a 5% significance level test? c. For the original sample sizes (50 passengers of each type) stated in the problem, what is the significance level that needs to be used in order to get a power of 90%? d. For the original sample sizes (50 passengers of each type) stated in the problem, and the rejection region ofXb )7; 2 0.075 (where X_b and 1?; are the sample means of the VOT for business- and leisure-passengers reSpectively), what is the power of the test