Question:

Statistical Abstracts (117th edition) reports that the average amount spent annually for food by householders under 25 years of age is $2,690. A random sample of 16 people under 25 years of age who live in a university neighborhood were surveyed. The survey showed that they spend a sample mean $3,220 with sample standard deviation $750. Test the claim that the mean for this neighborhood is greater than the national average. Use a 5% 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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