Question

A sample of 45 bottles of soft drink showed a variance of 1.1 in their contents. The process engineer wants to determine whether or not the standard deviation of the population is significantly different from 0.9 ounces. What is the value of the test statistic

Answer 1

Answer:

The value of the test statistic is 59.75.

Step-by-step explanation:

The test statistic for the population standard deviation is:

$\chi^2 = \frac{n-1}{\sigma_0^2}s^2$

In which n is the sample size, $\sigma_0$ is the value tested and s is the sample standard deviation.

A sample of 45 bottles of soft drink showed a variance of 1.1 in their contents.

This means that $n = 45, s^2 = 1.1$

The process engineer wants to determine whether or not the standard deviation of the population is significantly different from 0.9 ounces.

0.9 is the value tested, so $\sigma_0 = 0.9, \sigma_0^2 = 0.81$

What is the value of the test statistic

$\chi^2 = \frac{n-1}{\sigma_0^2}s^2$

$\chi^2 = \frac{44}{0.81}1.1 = 59.75$

The value of the test statistic is 59.75.