Question

N = 81 s2 = 625

H0: σ2 = 500
Ha: σ2 ≠ 500

The p-value is between

a. 0.025 and 0.05
b. 0.05 and 0.1
c. 0.1 and 0.2
d. 0.2 and 0.3

Answer 1

The p-value for testing whether the variance is different from 500 is between 0.1 and 0.2. Since the p-value is greater than the significance level of 0.05, the correct decision is not to reject the null hypothesis, indicating insufficient evidence to suggest a difference in variance.

Step-by-step explanation:

The question relates to hypothesis testing for variance using a chi-square distribution. The null hypothesis H0: σ2 = 500 is being tested against the alternative hypothesis Ha: σ2 ≠ 500. From the provided data, the p-value calculated is between 0.1 and 0.2.

When comparing the p-value to the significance level alpha (α), which is 0.05, the decision is to not reject the null hypothesis because the p-value is greater than alpha. This means there is insufficient evidence at the 5 percent level to conclude that the variance differs from 500.