Medicare spending per patient in different U.S. metropolitan areas may differ. Based on the sample data below, is the average spending in the northern region significantly less than the average spending in the southern region at the 1 percent level?

a) State the hypotheses and decision rule.

b) Find the test statistic assuming unequal variances.

c) State your conclusion. Is this a strong conclusion?

d) Can you suggest reasons why a difference might exist? (See The New Yorker [May 30, 2005], p. 38).

Medicare Spending per Patient (adjusted for age, sex, and race)

Statistic Northern Region Southern Region

Sample mean $3,123 $8,456

Sample standard deviation $1,546 $3,678

Sample size 14 patients 16 patients