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)StatisticNorthern RegionSouthern RegionSample mean$4,254$7,223Sample standard deviation$1,456$3,659Sample size12 patients15 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 >0b. H0: μN − μS ≥ 0 versus H1: μN – μS < 0 ab (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 if tcalc < . (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.) tcalc (c-1) Can we reject the null hypothesis? Yes, reject the null hypothesis.No, fail to reject the null hypothesis. (c-2) The average spending in the northern region is significantly less than the average spending in the southern region. TrueFalse

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MATLAB: An Introduction with Applications

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Author:Amos Gilat

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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	$4,254	$7,223
Sample standard deviation	$1,456	$3,659
Sample size	12 patients	15 patients

(a-1) Choose the appropriate hypotheses. Assume μ_N is the average spending in the northern region and μ_S is the average spending in the southern region.

a. H₀: μ_N − μ_S ≤ 0 versus H₁: μ_N – μ_S >0
b. H₀: μ_N − μ_S ≥ 0 versus H₁: μ_N – μ_S < 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.)

Reject the null hypothesis if t_calc < .

(b) Find the test statistic t_calc assuming 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.
No, fail to 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
False

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