The Health Department in a certain state investigated the difference in cost-to-charge ratio (the percentage of billed charges that are actual costs
to the hospital) between inpatients and outpatients among hospitals in
the state. Results are shown in the table. Test the null hypothesis that
there is no difference in the mean of ratios for all hospitals in the state
versus the alternative that the mean of the difference is positive. Use a =
.01. Assume a normal distribution of differences.
Hospital
1
2
3
4
5
6
Inpatient Outpatient
Ratio Ratio
68
54
100
75
71
53
74
56
100
74
83
71
Let d = Inpatient ratio - Outpatient ratio and
Hd = mean in the Inpatient ratio - mean in the Outpatient ratio.
The setup of the null and alternative hypotheses for this test
is