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 spent 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. .
(a) State the null and alternate hypotheses.
(b) Would you perform a left-tailed, right-tailed, or two-tailed test? Why?
c) Would you use a t critical value or a z critical value? Why?
(d) What is the critical value?
(e) Compute the test statistic.
(f) Sketch the normal curve indicating the positions of the critical value, critical region, and test statistic.
(g) Would you reject or fail to reject the null hypothesis?
(h) Interpret your conclusion in the context of this problem.