Question

A researcher performed a study to validate a translated version of the Western Ontario and McMaster University index (WOMAC) questionnaire used with spanish-speaking patients with hip or knee osteoarthritis. For the 76 women classified with severe hip pain, the WOMAC mean function score was 70.7 with a standard deviation of 14.6. We wish to know if we may conclude that the mean function score for a population of similar women subjects with severe hip pain is different from 75. Let α =0.01

Answer 1

The null and alternative hypothesis is ,

The test is two-tailed test.

Since , the population standard deviation is not known.

Therefore , use t-test.

Now , df=degrees of freedom=n-1=76-1=75

Teh critical values are ,

; The Excel function is , =TINV(0.01,75)

The test statistic is ,

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject Ho.

Conclusion : Hence , there is not sufficient evidence to conclude that the mean function score for a population of similar women subjects with severe hip pain is different from 75.