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 0.05 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: 6 0.012 0.002 0.6542 2.1966 0.6866 ​Error: 94 0.282 0.003 ​Total: 100 0.294 Should the null hypothesis that all the colors have the same mean weight be​ rejected? A. Yes​, because the​ P-value is greater than the significance level. B. No​, because the​ P-value is greater than the significance level. C. Yes​, because the​ P-value is less than the significance level. D. No​, because the​ P-value is less than the significance level. Does the company have a problem requiring corrective​ action? A. No​, because it is likely that the candies do not have equal mean weights. B. Yes​, because it is not likely that the candies do not have equal mean weights. C. No​, because it is not likely that the candies do not have equal mean weights. D. Yes​, because it is likely that the candies do not have equal mean weights.

Answer 1

The concept of ANOVA and hypothesis testing is needed as a prerequisite to understand the solution to this problem. The Solution is given below: