Question

Hypothesis test:
An experiment is conducted to study the effect of exercise on the reduction of cholesterol level in slightly obese patients considered to be at risk for a heart attack. Eight patients are put on a specified exercise regimen while maintain a normal diet. At the end of 4 weeks the change in cholesterol level was recorded. The program goal is to reduce the cholesterol by more than 25 points. At the end of the program the average reduction was actually 27. The standard deviation for the population is 18. Is there statistical evidence that the cholesterol dropped more than 25pts?

Answer 1

I'm just struggling to figure out what exactly I'm looking for such as mean, proportion, or variance. I never know what formula to use and how to determine what exactly I'm solving for.

Answer 2

You're conducting a test for the reliability of this program to reduce cholesterol. You make the claim that this program will reduce cholesterol by 25 points. In terms of a hypothesis, you're saying that cholesterol at time 0 is greater than current cholesterol levels by at least 25 points. Let \(c_0\) be the level at time 0, and \(c_1\) be the current level. The alternative hypothesis is that \(c_0-c_1\ge25\).

Usually, the null hypothesis would say that there is no change in the levels from then to now, i.e. \(c_0-c_1=0\), but in the context of the test you're running, \(c_0-c_1<25\) will suffice. (Note that this is a paired, one-tailed test.)

You're not explicitly given a significance level for the test, so I think we can assume \(\alpha=0.05\). Judging by the sample size, you'll be conducting a \(t\) test. I'd start by determining the rejection region.