Question

researchers conducted an experiment to test the effvts of alcohol. errors were recorded in a test of visual and motor skills for a treatment group of 21 people who drank ethanol and another geouo of 21 people given a placebo. the errors for the treatment group have a standard deviation of 2.40, and the errors for the placebo group have a standard deviation of 0.87. use a 0.05 significance level to test the claim that the treatment group has errors that are vary significally more than the errors of the placebo group. Assume that the two population are normally distributed.

Answer 1

Assuming that that the two population are normally distributed,

Let denote the variances within groups / errors of the subjects under the Treatment and Placebo groups respectively.

Given: ,

We have to test:

Vs   

The appropriate statistical test to test the above hypothesis, would be an F test for equality of variances; for which the test statistic is given by,

with critical region given by

Substituting the given values,

Comparing the test statistic with the critical value F for at 5% significance level which is equal to:

F(0.05,20,20) = 2.124 (From F table)

Since, F = 7.61 > 2.124 lie in the critical / rejection region, we may reject H0 at 5% level. We may conclude that the data provides sufficient evidence to support the claim that the treatment group has errors that are vary significally more than the errors of the placebo group.