Question

Two students are interested in whether or not there is variation in their test scores for math class. There are $15$total math tests they have taken so far. The first student’s grades have a standard deviation of $38.1$.The

second students' grades have a standard deviation of $22.5$. The second student thinks his scores are more consistent.

What is the F Statistic?

Short answer

The value of the F-statistic is calculated as follows$2.86$

Step-by-step solution

Given Information

The following information is given in the question, there are $15$total math tests they have taken so far. The first student’s grades have a standard deviation of $38.1$. The second students' grades have a standard deviation of $22.5$. What is the F Statistic?

Explanation

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

Explanation

$\text{2. Now enter the values of}S{x}_1=38.1n_1=15$

$S{\mathrm{x}}_2=22.5\text{and}{n}_2=15\text{then press ENTER.}$

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 value of F-statistic is$2.86$