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Expert-verified Found in: Page 767 ### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208 # 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 $38.1$.Thesecond students' grades have a standard deviation of $22.5$. The second student thinks his scores are more consistent.What is the F Statistic?

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

See the step by step solution

## Step 1: 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?

## Step 2: 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: ## Step 3: Explanation

$\text{2. Now enter the values of}S{x}_{1}=38.1{n}_{1}=15$

$S{\mathrm{x}}_{2}=22.5\text{and}{n}_{2}=15\text{then press ENTER.}$

The screenshot is given as below ## Step 4: 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 $2.86$ ### Want to see more solutions like these? 