Question

At the $5\%$significance level, what can we say about the cyclists' variances?

Short answer

The $P$-value is $0.387$and it is greater than the level of significance, so null hypothesis will be rejected. So, there is significance difference between the variance of two cyclists.

Step-by-step solution

Given information

The significance level is$5\%$. The significance level in the statistic is defined as the probability which the event will happen by possibility.

Explanation

To examine there is no dissimilarity between the variances of the two types of cyclists, use Ti-83 calculator. The method is state below:
Click on STAT $\to$arrow over the TESTS $\to$arrow down to 2 -sample $F$-test $\to$ENTER $\to$arrow to the Stats and press ENTER. Then it will be:

Explanation

Then, enter the values of$5{\mathrm{x}}_1=\sqrt{23.8},n_1=35,5{\mathrm{x}}_2=\sqrt{32.1,}$and $n_2=35$then press ENTER. Then it will be:

Explanation

Then select the hypothesis as $H_1:{\sigma }_1<{\sigma }_2$and press ENTER. Then arrow down to calculate, press ENTER. It will be,