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 an iPhone 11 costs with the iPhone 14 now released

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 an iPhone 11 costs with the iPhone 14 now released.  After some debate, they decide that the average (mean) price should be less than $400 but that there is likely going to be a large amount of variability in the prices since there are multiple newer models available.  A sample of 16 phones has the following costs: 

330       382       357       319       349       380       359       345
449       515       349       328       344       429       358       479

1. Use the data provided above to test her friends' claim about the price of an iPhone 11.  Show and label all six steps using either the critical region approach or the p-value approach. Use α = 0.05
2. Use the sample to construct a 90% confidence interval to estimate the mean price of an iPhone 11.  Write the corresponding confidence statement for this interval.  Are the values in your CI expected based on the conclusion from the hypothesis test?  Explain.
3. With the large, expected variability in iPhone 11 prices, perform a hypothesis test to determine if the standard deviation of iPhone 11 prices is at least $50.  Use α = 0.05.
4. What assumptions are being made to run the hypothesis tests in parts a) and c)?