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. Is the claim accurate?

Short answer

The p-value is $0.47$ which is greater than the level of significance of $0.10$, so the null hypothesis of no difference between the variance of the two types will be accepted. Thus, there is no variation in the drive times for the two types of workers.

Step-by-step solution

GIven Information

In the following question, it is stated 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.Is the claim accurate?

Explanation

To check that the claim is valid, use the Ti-$83$ calculator. The procedure is shown 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

$\text{2. Now enter the values of}5x_1=\sqrt{12.1}$

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

Explanation

3. 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 p-value is $0.47$which is greater than the level of significance of $0.10$, so the null hypothesis of no difference between the variance of the two types will be accepted . Thus, there is no variation in the drive times for the two types of workers.