Question

Two coworkers commute from the same building. They are interested in whether or not there is any variation in the time it takes them to drive to work. They each record their times for $20$commutes. The first worker’s times have a variance of $12.1$. These coworkers' times have a variance of $16.9$. The first worker thinks that he is more consistent with his commute times. Test the claim at the$10$% level. Assume that commute times are normally distributed. What is the F statistic?

Short answer

From the information, we observed the value of the F-statistic is $0.72$

Step-by-step solution

Given Information

It is given in the problem that, they each record their times for $20$commutes. The first worker’s times have a variance of $12.1$. These coworkers' times have a variance of $16.9$. Test the claim at the$10$% level. What is the F statistic?

Explanation

To compute the value of the F-Statistic, use the Ti-$83$ calculator. The method is given as below:

1. Click on the STAT $\to$arrow over the TESTS $\to$arrow down to $2$-sample $F$-test $\to$ENTER $\to$arrow to the Stats and press ENTER. The screenshot is given below:

Explanation

$\text{Now enter the values of}S{x}_1=\sqrt{12.1}$

$n_1=20S{\mathrm{x}}_2=\sqrt{16.9}\text{and}{n}_2=20\text{then press}$ENTER. The screenshot is given as below:

Step 4: Explanation

Select the hypothesis as $H_1:{\sigma }_1<{\sigma }_2$and press ENTER. Then arrow down to calculate, and press ENTER. The screenshot of the obtained output is given as below:

Thus, the value of the F-statistic is $0.72$