Suppose 50 billing statements from the computer databases of the Marriott and Westin hotel chains and the nightly room rates were recorded. The sample data is shown in the table below: Marriott Westin Sample Average ($) 150 165 Sample Standard Deviation ($) 35 45 (a) Conduct a statistical hypothesis that the mean price of the Westin hotels is greater than the Marriott hotels by calculating the associated p-value. (Clearly state all assumptions/theorems and show all your work) (b) Suppose you were not acting ethically and wanted to change your approach from part (a) to the rejection region approach. Having already computed the p-value, what is the smallest value of the significance level that you could choose to ensure that you "had evidence" to reject the null hypothesis