Discuss the below:
Q: Quart cartons of milk should contain at least 32 ounces. A sample of 22 cartons contained the following amounts in ounces.
31.5 32.2 31.9 31.8 31.7 32.1 31.5 31.6 32.4 31.6 31.8
32.2 32.1 32.1 31.6 32.0 31.6 31.7 32.0 31.5 31.9 32.8
a) What set of hypotheses should be tested if we want to demonstrate the mean amount of milk in all cartons of this brand is actually less than 32 ounces?
b) Select the distribution to use. Explain briefly why you selected it.
c) Assuming that they wish to test the claim at a = 0.025, determine the rejection and non rejection regions based on your hypotheses in a). State the critical value.
d) Calculate the value of the test statistic. What does the p-value mean for this problem? Explain.
e) Applying the hypothesis test, can we conclude that there is sufficient evidence to claim that the mean amount is less than 32 ounces in all cartons of this brand?