Question: Problem 25)

Ruth is concerned about the spending habits of teens. She read a report that the national weekly spending average for teens in the age group 12 to 15 years is $42. She took a random sample of 60 teens that live in a rural area and found that they spent an average of $36 per week with sample standard deviation $7.50. Test the claim that rural teens from this area spend less than the national average. Use a 1% significance level.

a. State the null and the alternate hypothesis.

b. Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution. Find the critical values.

c. Compute the z or t value of the sample test statistic.

d. Find the P value or an interval containing the P value for the sample test statistic.

e. Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level. Explain your conclusion in simple, nontechnical terms.