Medicare spending per patient in different U.S. metropolitan areas may differ. B
ID: 3156788 • Letter: M
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)
$7,307
1) Choose the appropriate hypotheses. Assume N is the average spending in the northern region and Sis the average spending in the southern region. Please choose one.
A) H0: N S 0 versus H1: N – S < 0
B) H0: N S 0 versus H1: N – S >0
2) Specify the decision rule. (Use quick rule to determine degrees of freedom. Round your answer to 3 decimal places. Negative value should be indicated by a minus sign.)
Reject the null hypothesis if tcalc < __________. (Fill in the blank).
3) Find the test statistic tcalc assuming unequal variances. (Round your answer to 2 decimals places. Negative value should be indicated by a minus sign.)
tcalc = ___________ (Fill in the blank)
Statistic Northern Region Southern Region Sample Mean $3,914$7,307
Sample Standard deviation $1,449 $3,506 Sample size 14 patients 17 patientsExplanation / Answer
A) H0: N S 0 versus H1: N – S < 0
df = 14 + 17 - 2 = 29
critical vlaue = - 2.462
reject Ho if T < -2.462
T = ( 3914 - 7307 ) / ( srqt 1449^2 / 14 + 3506^2 / 17 )
T = -3.63
since t < critical value we reject Ho