The manager of a department store disputes the company’s claim that the average age of customers who buy a particular brand of clothes is 16; she believes the average age is older than 16. A clerk for the store stops the next 25 people buying these clothes and asks for their age. She calculates a mean age of 18.50 years, with a standard deviation of 2.25 years. Use the data from this sample to test the manager’s claim.

a. State the null and alternative hypotheses (H₀ and H₁) (allow for the possibility that the average age may be younger than 16).

b. Make a decision about the null hypothesis.
(1) Calculate the degrees of freedom (df ).
(2) Set alpha (α), identify the critical values (draw the distribution), and state a decision rule.
(3) Calculate a statistic: t-test for one mean.
(4) Make a decision whether to reject the null hypothesis.
(5) Determine the level of significance.

c. Draw a conclusion from the analysis.

d. Relate the result of the analysis to the research hypothesis.