A golfer would like to test the hypothesis that the variance of his golf score equals 10.0. A random sample of 28 rounds of golf had a sample standard deviation of 3.5. The test statistic for this hypothesis test would be ______
A)12.57
B)46.23
C)33.08
D)40.75

Question

Quizplus · Accepted Answer

The test statistic for testing a hypothesis about a population variance ($\sigma^2$) is given by the formula $\chi^2 = \frac{(n-1)s^2}{\sigma^2}$, where $n$ is the sample size, $s^2$ is the sample variance, and $\sigma^2$ is the hypothesized population variance. Here, $n = 28$, $s = 3.5$ (so $s^2 = 3.5^2 = 12.25$), and $\sigma^2 = 10.0$. Plugging these values into the formula gives $\chi^2 = \frac{(28-1) \times 12.25}{10} = \frac{27 \times 12.25}{10} = 33.075$, which rounds to 33.08.

A Golfer Would Like to Test the Hypothesis That the Variance