Question

Researchers conducted an experiment to test the effects of alcohol. The errors were recorded in a test of visual and motor skills for a treatment group of 24 people who drank ethanol and another group of 22 people given a placebo. The errors for the treatment group have a standard deviation of 1.82​, and the errors for the placebo group have a standard deviation of 1.53. Use a 0.05 significance level to test the claim that the treatment group has errors that vary more than the errors of the placebo group. Assume that both samples are independent simple random samples from populations having normal distributions. Identify the test statistic. F=_____ The P-value is ______

Answer 1

It has been given that

One Group of 24 people who drank ethanol is given by n1

Another group of 22 people given a placebo which is given by n2

Errors for treatment group has standard deviation 1.82 which is indicated by S1

errors for the placebo group have a standard deviation of 1.53 which is indicated by S2

The claim is that  treatment group has errors that vary more than the errors of the placebo group

Because the null hypothesis is hypothesis of equality

So our claim will become alternative hypothesis & equality will become null hypothesis

So let us suppose the hypothesis

Null hypothesis Ho:

Alternate hypothesis Ha:

It has also been given that level of significance is 0.05

and samples are independent and normal populations

So test stat is given as

Let us find the critical region using the excel function

Because our test is one tail test

Test statstic assumes that F distribution with numerator of degree of freedom n1-1=24-1=23 and denominator degree of freedom will be n2-1=22-1=21

We would use the function =FINV(0.05,23,21)

So Critical value of F will be 2.06

To find the p value for the test using the excel function =FDIST(1.41,23,21)

So value of p is 0.216

Because value of p is greater than level of significance 0.05

and also test statstic(1,41) is less than critical value 2.06

Thus test statstic does not lie in critical region

We fail to reject the null hypothesis

There is insufficient evidence that treatment group has errors that vary more than errors of placebo group