SOLUTION: Medicare spending per patient in different U.S. metropolitan areas may differ. Based on the sample data below, is the average spending in the northern region significantly less tha

Question 247011: Medicare spending per patient in different U.S. metropolitan areas may differ. Based on the sample data below, is the average spending in the northern region significantly less than the average spending in the southern region at the 1 percent level? (a) State the hypotheses and decision rule. (b) Find the test statistic assuming unequal variances. (c) State your conclusion. Is this a strong conclusion? (d) Can you suggest reasons why a difference might exist?
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
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Medicare spending per patient in different U.S. metropolitan areas may differ. Based on the sample data below, is the average spending in the northern region significantly less than the average spending in the southern region at the 1 percent level?
(a) State the hypotheses and decision rule.
Ho: u(south)-u(north) > 0
H1: u(south)-u(north) <= 0
Rule: Reject Ho if p-value < 1%
------------------------------------------
(b) Find the test statistic assuming unequal variances.
I ran a 2 Sample t-test and got the following:
ts = 5.2903
p = 100%
---------------------
(c) State your conclusion. Is this a strong conclusion?
Since the p-value is greater than 1%, fail to reject Ho.
North average is is much less than south average.
-----
(d) Can you suggest reasons why a difference might exist?
I'll leave that to you.
---------------------------------------------------------------------
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
==================================================================
Cheers,
Stan H.
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