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 _____.
A) 400
B) 22.99
C) 4.85
D) 20

Question

Quizplus · Accepted Answer

The test statistic for testing a claim about a population standard deviation (σ) when the sample standard deviation (s) is known, is calculated using the formula: $\chi^2 = \frac{(n-1)s^2}{\sigma^2}$, where $n$ is the sample size, $s$ is the sample standard deviation, and $\sigma$ is the claimed population standard deviation. Here, $n = 20$, $s = 0.11$, and $\sigma = 0.1$. Plugging these values into the formula gives: $\chi^2 = \frac{(20-1)(0.11)^2}{(0.1)^2} = 22.99$.

The Producer of a Certain Medicine Claims That Its Bottling