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 s_$2$ in this problem?

Short answer

From the information is given in question, s₂ is calculated as $4.11$

Step-by-step solution

Step 1: Given Information

The following information is given in the problem, each of them records 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 s_$2$ in this problem?

Explanation

To compute the value ^s$2$, use the Ti-$83$ calculator. The procedure 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

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

$n_1=20,S{\mathrm{x}}_2=\sqrt{16.9}\text{and}{n}_2=20\text{then press}$ENTER.

The screenshot is given below

Explanation

3. Select the hypothesis as H_$1$:${\sigma }_1<{\sigma }_2$press ENTER. Then arrow down to compute, and press ENTER. The screenshot of the obtained output is given below:

Thus, the value of Sx₂ is$4.11$