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.

State the null and alternative hypotheses.

Short answer

The null hypothesis and alternative hypothesis is as shown below:

$H_0:{\sigma }_1={\sigma }_2$

$H_1:{\sigma }_1<{\sigma }_2$

Step-by-step solution

Given Information

This 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 $22.5$. State the null and alternative hypotheses.

Step 2: Explanation

Our Null hypothesis is based on there being no significant difference between the variations of scores for math class.

So, we have

$H_0:{\sigma }_1={\sigma }_2$

The alternative hypothesis is

$H_1:{\sigma }_1<{\sigma }_2$