State the null and alternative hypotheses (Ho and H1)–be sure to allow for the possibility that the average age may be younger than 16.

Two researchers test the same research hypothesis using the same instruments.  One researcher rejects the null hypothesis but the other does not.

a. Which researcher is more likely to have had a larger sample size?  Explain why you think so.

b. Which researcher is more likely to have had a smaller level of alpha (  )?  Explain why you think so.

c. Which researcher is more likely to have had a directional alternative hypothesis?  Explain why you think so.

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 their age.  She calculates a mean of 18.5 years, with a standard deviation of 2.25 years.  Use this summary data calculated from the sample of 25 people to test the manager’s claim.  Follow the steps in section 7.6 of the textbook to carry out the following.

a. State the null and alternative hypotheses (H_o and  H₁)–be sure to 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 (), identify the critical values (it may be helpful to draw the distribution, but you need not turn that in), and state the decision rule
3. Calculate the test statistic: t-test for one mean
4. Make your decision about 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 (the hypothesis expressed in words)