A clothing retailer is planning to sell a new range of high-quality hats in the U.K., each at a retail price of E89. However, one of the marketing managers believes this price may be too low if it is to signal high quality. The company has performed a market research in a random sample of 70 members of the target population. The market research asked which price was necessary, at a minimum, to signal high quality and differentiate the hats from lower-quality alternatives. The sample mean was $97.61, while the sample standard deviation was $23.47. a. Using the p-value to assess significance against a = 0.05, is there statistical evidence to suggest that the proposed retail price of $89 is too low? (5 marks) The marketing team decides it prefers to start selling hats at a price that is too high rather than a price that is too low to signal high quality. b. Between Type I and Type II errors, which does the company prefer? (5 marks) On reflection, the marketing team realises that the decision to sample 120 members of the target population was made without much systematic thought. It believes that from now on, decisions about sample sizes are to be made in such a way that the margin of error is $3.50 at 99% confidence. c. Applying this criterion, what should have been the minimum sample size in the case of this particular range of hats? Assume that $23.47 is the population standard deviation