Need explanation, answers, six step hypothesis tes along with minitab instructions

1. After breaking her phone and not being eligible for a new phone under her plan a woman asks her friends how much they think a used iPhone 11 costs. After some debate they decide that the average (mean) price should be no more than $400 with the iPhone 12 hitting the market. A sample of 16 phones has they following costs:

515 485 305 485 350 310 360 295 580 540 515 480 320 465 345 380

a) Use the data provided above to test her friends' claim about the price of a used iPhone 11. Show and label all six steps using the critical region approach (do not use the p-value). Use = 0.05

b) Use Minitab to run the hypothesis test from part a) to obtain the p-value. Use the p-value to make and explain your decision about the hypotheses. Does your decision agree with part a)? Include the Minitab output as part of your exam.

c) Use the sample to construct a 95% confidence interval to estimate the average price of a used iPhone 11. Give a written interpretation of this interval. Are the values in your CI expected based on the conclusion from the hypothesis test? Explain.

d) What assumptions are being made to run the tests in parts a) and b) and to determine the confidence interval in part c)?

e) How many iPhones would be needed sampled to estimate the mean price of a used iPhone 11 with a 95% confidence interval to within $25? Use s from the sample to approximate .