Question

Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 23 people who drank ethanol and another group of 23 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 0.72. Use a 0.05 significance level to test the claim that the treatment group has errors that vary significantly more than the errors of the placebo group. Assume that the two populations are normally distributed.

What is the test statistic:

What is the p-value:

Answer 1

a) The test statistic here is computed as:

b) The p-value here is computed for 23-1, 23-1 that is 22,22 degrees of freedom from the F distribution tables as:

Therefore the p-value is approximately 0

This shows that the test is significant and we have sufficient evidence to reject the fact that the 2 standard deviations are same. Therefore we have sufficient evidence to support the claim that the treatment group has errors that vary significantly more than the errors of the placebo group