Two cyclists are comparing the variances of their overall pa

Two cyclists are comparing the variances of their overall paces going uphill. Each cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of 23.8 and the second cyclist has a variance of 32.1. The cyclists want to see if their variances are the same or different. State the null and alternate hypotheses. What is the F Statistic? At the 5% significance level, what can we say about the cyclists

Solution

Let o1^2 be the variance for first cyclist

Let o2^2 be the variance for second cyclist

Null hypothesis: o1^2=o2^2

Alternative hypothesis: o1^2 not equal to o2^2

The test statistic is

F=s1^2/s2^2

=23.8/32.1

=0.74

Given a=0.05, the critical values are F(0.025, df1=1, df2=2)=0.00 (from F table)

F(0.975, df1=1, df2=1)=647.789(from F table)

The rejection regions are if F<0 or F>647.789, we reject Ho.

Since F=0.74 is between 0 and 647.789, we do not reject Ho.

So we can conclude that their variances are the same