4. (15p) A test will be conducted to see how long a seven-ounce tube of toothpaste lasts. The researcher wants to establish that the mean time u is greater than 30.5 days. From a random sample of size 75, an investigator obtains sample mean xbar = 32.3 days and sample st dev s = 6.2 days. (a) Formulate the null and alternative hypothesis, calculate the p-value and your conclusions. (b) Do you think the p-value will change if you assumed that the parent distribution is assumed to be normal? (c) Explain the errors you might make in this hypothesis test and, in particular, calculate the power of the test when a = 0.02, and the true mean u is 34 days