Question:

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.

1. State the null and the alternate hypothesis.
2. Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution. Find the critical values.
3. Compute the z or t value of the sample test statistic.
4. Find the P value or an interval containing the P value for the sample test statistic.
5. 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.

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