Question

The producer of a certain medicine claims that its bottling equipment is very accurate and that the standard deviation of all its filled bottles is 0.1 ounce or less. A sample of 20 bottles showed a standard deviation of .11. The test statistic to test the claim is _____.

Answer 1

Answer: The test statistic to test the claim is $\chi^2=22.99$.

Step-by-step explanation:

Let $\sigma$ be the standard deviation of filled bottles.

As per given , we have

$H_0:\sigma=0.1\\\\ H_1:\sigma\neq0.1$

To fins test statistic , we use Chi -square test for population standard deviation:

$\chi^2=\dfrac{(n-1)s^2}{\sigma^2}$

, where n= sample size .

s= sample standard deviation.

We are given that , n= 20 and s= 0.11

Then, $\chi^2=\dfrac{(20-1)(0.11)^2}{(0.1)^2}$

$\chi^2=\dfrac{(19)(0.0121)}{0.01}=22.99$

Hence, the test statistic to test the claim is $\chi^2=22.99$.