Question

the measurements of the diameters (in inches) of 12 randomly chosen golf balls are listed. at α=0.05, is there enough evidence to reject the claim that the standard deviation of the measurements of these diameters is 0.005? assume the population is normally distributed. 1.677 1.682 1.681 1.679 1.677 1.681 1.682 1.678 1.677 1.682 1.679 1.678 click the icon to view the chi - square distribution table. (d) decide whether to reject or fail to reject the null hypothesis. a. fail to reject h₀. the standardized test statistic is not in the rejection region. b. fail to reject h₀. the standardized test statistic is in the rejection region. c. reject h₀. the standardized test statistic is in the rejection region. d. reject h₀. the standardized test statistic is not in the rejection region. (e) interpret the decision in the context of the original claim. is there enough evidence to reject the claim at the 5% level of significance? a. no, since the null hypothesis is rejected, there is enough evidence to reject the claim. b. yes, since the null hypothesis is rejected, there is enough evidence to reject the claim. c. no, since the null hypothesis is not rejected, there is not enough evidence to reject the claim. d. yes, since the null hypothesis is not rejected, there is not enough evidence to reject the claim.

Explanation:

Part (d)

In hypothesis testing, we reject the null hypothesis (\( H_0 \)) when the test statistic lies in the rejection region (determined by the significance level \( \alpha = 0.05 \) and the chi - square distribution for this standard deviation test). Option C correctly states that we reject \( H_0 \) because the test statistic is in the rejection region. Options A and B are wrong as we do reject \( H_0 \), and option D is wrong because if we reject \( H_0 \), the test statistic must be in the rejection region.

Part (e)

The original claim is about the standard deviation. The null hypothesis (\( H_0 \)) is related to the claim (that the standard deviation is 0.005). When we reject \( H_0 \) (as we did in part (d)), this means that at the 5% significance level, we have enough evidence to reject the original claim. Option A is wrong in its "No" conclusion, option C is wrong as we did reject \( H_0 \), and option D is wrong in both the "Yes" (misplaced) and the non - rejection of \( H_0 \) part.

Answer:

C. Reject \( H_0 \). The standardized test statistic is in the rejection region.