51. An extensive study of the cost of health care in the United States presented data showing that the mean spending per Medicare enrollee in 2003 was $6883 (Money, Fall 2003). To investigate differences across the country, a researcher took a sample of 40 Medicare enrollees in Indianapolis. For the Indianapolis sample, the mean 2003 Medicare spending was $5980 and the standard deviation was $2518.

a. State the hypotheses that should be used if we would like to determine whether the mean annual Medicare spending in Indianapolis is lower than the national mean.

b. Use the preceding sample results to compute the test statistic and the p-value.

c. Use α  .05. What is your conclusion?

d. Repeat the hypothesis test using the critical value approach.