Medicare spending per patient in different U.S. metropolitan areas may differ. Based on the sample data below, answer the questions that follow to determine whether the average spending in the northern region is significantly less than the average spending in the southern region at the 1 percent level. Medicare Spending per Patient (adjusted for age, sex, and race) Statistic Northern Region Southern Region Sample mean $ 4,324 $ 7,426 Sample standard deviation $ 1,537 $ 3,495 Sample size 11 patients 18 patients (a-1) Choose the appropriate hypotheses. Assume μN is the average spending in the northern region and μS is the average spending in the southern region. a. H0: μN − μS ≤ 0 versus H1: μN − μS >0 b. H0: μN − μS ≥ 0 versus H1: μN − μS < 0 (a-2) Specify the decision rule. (Use the quick rule to determine degrees of freedom. Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.) (b) Find the test statistic tcalc assuming unequal variances. (Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.) (c-1) Can we reject the null hypothesis? (c-2) The average spending in the northern region is significantly less than the average spending in the southern region.
Medicare spending per patient in different U.S. metropolitan areas may differ. Based on the sample data below, answer the questions that follow to determine whether the average spending in the northern region is significantly less than the average spending in the southern region at the 1 percent level.
| Medicare Spending per Patient (adjusted for age, sex, and race) | ||
| Statistic | Northern Region | Southern Region |
|---|---|---|
| Sample mean | $ 4,324 | $ 7,426 |
| Sample standard deviation | $ 1,537 | $ 3,495 |
| 11 patients | 18 patients |
(a-1) Choose the appropriate hypotheses. Assume μN is the average spending in the northern region and μS is the average spending in the southern region.
a. H0: μN − μS ≤ 0 versus H1: μN − μS >0
b. H0: μN − μS ≥ 0 versus H1: μN − μS < 0
(a-2) Specify the decision rule. (Use the quick rule to determine degrees of freedom. Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)
(b) Find the test statistic tcalc assuming unequal variances. (Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.)
(c-1) Can we reject the null hypothesis?
(c-2) The average spending in the northern region is significantly less than the average spending in the southern region.
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