Question

Suppose our hospital is concerned about the delay in transferring older patients to long-term institution after hospitalization. We are concerned that the delay in discharges from Hospital 1 is longer than Hospital 2. To Evaluate our concern, we randomly select 15 recent discharges from each hospital and measured, in days the length of the delay. The result of the two sample as follow:

Hospital 1: 15, 13, 16 , 19, 10, 22, 23, 19, 18, 17, 15, 19, 16, 12, 8

Hospital 2: 10, 13, 16, 18, 12, 9, 18, 15, 19, 11, 13, 9, 19, 15, 18, 20

if α =0.05, use the data to evaluate the claim. Assume the Population variances are not equal.

Answer 1

For two sample mean test with unequal variances, two things will change compared to other tests

1. The standard error for the test statistic

2. The degrees of freedom for the t test

Null hypothesis is : the difference between means is equal to zero, Mu1 - Mu2 = 0

where

xbar = mean of hospital 2 : 14.6875

ybar = mean of hospital 1: 16.1333

sx2 = variance of hospital 2: 14.23 (use sample variance)

sy2 = variance of hospital 1: 17.41

t = -1.0098

degrees of freedom = 28.138 = 29

t critical = -2.37 for two-sided test

Since t value does not fall beyond t critical region, we fail to reject null hypothesis. Or in other words, the mean between hospital 1 and 2 are same