Tests of Hypotheses

[Starling]

I am having a hard time setting up this problem:

A grade-school teacher has obtained the following figures for the time (in minutes) that 10 randomly picked students in her class took to complete an assigned task.

15 10 12 8 11 10 10 13 12 9

At the 5 percent level significance, is the true variance of the time different from 2.4 minutes squared? Assume a normal distribution.

If anyone can offer some help to get started that would be awesome! Thank you! :wink:

 

[JakeD]

Use the test statistic

\(\displaystyle \large \chi = \frac{\sum_{i=1}^{n} (X_i - \bar{X})^2}{\sigma^2}\).

Assuming a normal distribution, \(\displaystyle \chi\) has a chi-square distribution with \(\displaystyle n -1\)degrees of freedom. (This is from the derivation of the t-statistic.) Under the null hypothesis, \(\displaystyle \sigma^2 = 2.4^2 .\)