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 $ 3,123 $ 8,456 Sample standard deviation $ 1,546 $ 3,678 Sample size 14 patients 16 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 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 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) State your conclusion. We (Click to select) can cannot conclude that the average spending in the northern region is significantly less than the average spending in the southern region. (c-2) Is this a strong conclusion? multiple choice 3 Yes No

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 1GP

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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	$	3,123		$	8,456
Sample standard deviation	$	1,546		$	3,678
Sample size		14	patients		16	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

multiple choice 1

(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) State your conclusion.

We   (Click to select)   can   cannot  conclude that the average spending in the northern region is significantly less than the average spending in the southern region.

(c-2) Is this a strong conclusion?

multiple choice 3

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