91Ó°ÊÓ

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?

To compute the value ^s$2$, use the Ti-$83$ calculator. The procedure is given as below:

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

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

3. Select the hypothesis as H_$1$:${\mathrm{σ}}_1<{\mathrm{σ}}_2$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$4.11$