Question

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	$3,955	$7,083
Sample standard deviation	$1,493	$3,647
Sample size	11 patients	17 patients

(a)	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 b

(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

Answer 1

a)

b. H₀: μ_N − μ_S ≥ 0 versus H₁: μ_N – μ_S < 0

b)

x1                     =	3955.000	x2                    =	7083.000
s1                     =	1493.000	s2                    =	3647.000
n1                    =	11.000	n2                    =	17.000
Point estimate =x1-x2=			-3128.000

standard error se=√(S21/n1+S22/n2)=			992.4866
test stat t calc=(x1-x2-Δo)/Se=		-3.15