Final answer:
The test statistic for a chi-square test with a sample size of 14, sample standard deviation of 20, and null hypothesis variance of 500 should be 10.40. However, since this number does not match any of the options provided, there may be an error in the question or the options.
Step-by-step explanation:
The subject in question involves performing a hypothesis test to determine whether the variance of a population is greater than or equal to a specified value. Given a sample size (n = 14), sample standard deviation (s = 20), and the null hypothesis being (σ² ≤ 500), we need to calculate the test statistic for a chi-square distribution with degrees of freedom df = n - 1, which in this case is df = 13. The test statistic is calculated using the formula:
chi-square test statistic = χ² = (n - 1)s² / σ²
Plugging in the values, we get:
chi-square test statistic = (14 - 1) * 20² / 500 = 13 * 400 / 500 = 5200 / 500 = 10.40
However, since this value does not match any of the answer options provided in the initial question, it appears that there may be an error in the question itself or in the provided options. It's important to carefully review the calculation and ensure the values and hypotheses given are as intended.