Question

A sample of colored candies was obtained to determine the weights of different colors. The ANOVA table is shown below. It is known that the population distributions are approximately normal and the variances do not differ greatly. Use a 0.025 significance level to test the claim that the mean weight of different colored candies is the same. If the candy maker wants the different color populations to have the same mean weight, do these results suggest that the company has a problem requiring corrective action? Source: DF: SS: MS: Test Stat, F: Critical F: P-Value: Treatment: 4 0.024 0.006 2.7668 2.9483 0.0328 Error: 81 0.162 0.002 Total: 85 0.186 Should the null hypothesis that all the colors have the same mean weight be rejected? O A. No, because the P-value is less than the significance level. O B. No, because the P-value is greater than the significance level. C. Yes, because the P-value is less than the significance level. OD. Yes, because the P-value is greater than the significance level. Does the company have a problem requiring corrective action? OA. No, because it is likely that the candies do not have equal mean weights. OB. No, because it is not likely that the candies do not have equal mean weights. OC. Yes, because it is not likely that the candies do not have equal mean weights. OD. Yes, because it is likely that the candies do not have equal mean weights.

Answer 1

a) Given P-value = 0.0328
alpha = 0.025

since p-value > alpha 0.025 so we accept the null hypothesis

Correct answer: Option (B) No, because the P-value is greater than the significance level.

b) Correct answer: Option (B) No because it is not likely that the candies do not have equal mean weights