Question

A knee surgeon collected data on the post-operative hemoglobin levels (in g/dL) of 102 patients who had total knee replacements. He randomly assigned half of the patients to receive a closed suction drain and half to receive no drain. Of interest is whether post operative hemoglobin levels, on average, differed between the drain and no drain groups The data are available in the file knee.csv.

a. What are the null and alternative hypotheses? 

b. What is the value of the test statistic? 

c.  What is the approximate p-value? 

d.  Using a significance level of a = 0.05, state your conclusions in the language of the problem.

e.  Describe two key assumptions required for the validity of your hypothesis test and explain why they are reasonable in this setting

Answer 1

Here we are to understand whether on an average post operative hemoglobin levels differed between drain and no drain groups.

a) we have;

as our null and alternative hypothesis respectively, where are the population means of post operative hemoglobin for drain and no drain groups.

b) The test statistic is given by,

c) since the sample size is large by CLT the test statistic follows z test.

the p-value is given by- from the Z table and then multiply it with 2 since this is a two sided test.

d) at significance level of 0.05 the critical value is 1.96.

if the p value is less than 0.05 then we reject the null hypothesis.

e) we assume that since the variance is unknown. this is known as the assumption of homoscelasticity.

Because of the large samples, the central limit theorem permits calculation of the z score as opposed to using t. The z score is calculated using the given sample standard deviations.
If the assumptions are correct and is true, the test statistic is approximately normally distributed.