Question

To investigate an alleged unfair trade practice, the Federal Trade Commission (FTC) takes a random sample of sixteen “5- ounce” candy bars from a large shipment. The mean of the sample weights is 4.85 ounces and the sample standard deviation is 0.1 ounce. It is reasonable to assume the population of candy bar weights is approximately Normally distributed. Based on this sample, does the FTC have grounds to proceed against the manufacturer for the unfair practice of short-weight selling, on average? Answer this question by completing the following steps of a hypothesis test at the 5% significance level.

a. State the null and alternative hypotheses.

b. obtain the value of the test statistic.

c. obtain the p-value

Answer 1

a) The hypotheses are:

Rejection region:

Reject Ho if T <t_{0,05, 15} Where 15 is the degree of freedom n-1

b) Test statistic:

c) P-value:

P-value computed using the T table shown below as

P-value=0.000 almost 0

Conclusion:

Since the P-value << 0 hence we reject the null hypothesis and conclude that there is enough evidence to support the claim,