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Item11

Item 11 2 points

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$4,463$7,313Sample standard deviation $1,496 $3,488Sample size 13 patients 16 patients

Northern Region

Sample Mean $4,463 - Sample Standard Deviation $1,496 - Sample Size 13

Southern Region

Sample Mean $7,313 - Sample Standard Deviation $3,488 Sample Size 16

(a-1)Choose the appropriate hypotheses. Assume_Nis the average spending in the northern region and_Sis the average spending in the southern region.

a.H₀:_NS 0 versusH₁:_N-_S>0

b.H₀:_NS 0 versusH₁:_N-_S< 0

multiple choice 1

• a
• b

(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.)

Reject the null hypothesis ift_calc<.

(b)Find the test statistict_calcassuming unequal variances.(Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.)

t_calc

(c-1)Can we reject the null hypothesis?

Yes, reject the null hypothesis.

(c-2)The average spending in the northern region is significantly less than the average spending in the southern region.

True