A chips company claims that their "vinegar and salt" chips bags have a mean weight of 5 ounces following a normal distribution. To test this hypothesis, you select a random sample of 16 bags and find...

Extracted text: A chips company claims that their "vinegar and salt" chips bags have a mean weight of 5 ounces following a normal distribution. To test this hypothesis, you select a random sample of 16 bags and find that the mean and standard deviation of this sample are 4.7 ounces and 0.5 ounces, respectively. (a) Use a significance level 0.01 to test the above hypothesis. What is your conclusion? (you need to clearly state the null and alternative hypotheses and show all the necessary steps to get the full score). (b) Illustrate the critical region for the above test. ( (c) Find a 90% confidence interval for the population variance. ( (d) Assume in the main problem description, the population standard deviation was known to be 0.7. Using this new information, calculate the p-value of the test based on the same sample information and hypothesis. Based on the calculated p-value and the significance level of 0.1, what conclusion do you make?