The FTC periodically conducts statistical studies

The FTC periodically conducts statistical studiesQuestion
The FTC periodically conducts statistical studies designed to test the claims that manufacturers make about their products. The label on a large can of Hilltop Coffee states that the can contains three pounds of coffee. The FTC interprets the label information as a claim by Hilltop that the average filling weight is at least three pounds per can. The process standard deviation is known to be 0.18 pounds. A random sample of 36 large Hilltop coffee cans is selected. The resulting sample mean is 2.92 pounds.

a. State the null and alternative hypotheses that should be used to test Hilltop’s claim.

b. Are there any assumptions required to conduct this test? If so, what are they?

c. If we use a level of significance of 1%, to test Hilltop’s claim, how should this significance level be interpreted?

d. Using a level of significance of 1%, test Hilltop’s claim.

e. What is the p-value of this test?

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