Length of Hospital Stays: The average length of “short” hospital stays for men is slightly longer thatn that for women: 5.2 days vs. 4.5 days. A random sample of recent hospital stays for both men and women revealed the following. At ? = 0.01, is there sufficient evidence to conclude that the average hospital stay for men is longer than the average hospital stay for women?

Question

Length of Hospital Stays: The average length of “short” hospital stays for men is slightly longer thatn that for women: 5.2 days vs. 4.5 days. A random sample of recent hospital stays for both men and women revealed the following. At ? = 0.01, is there sufficient evidence to conclude that the average hospital stay for men is longer than the average hospital stay for women?
 MEN WOMEN
 Sample Size 32 30
 Sample Mean 5.5 days 4.2 days
 Pop. Standard Deviation 1.2 days 1.5 days

PsyDAG · Answer

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.