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

Please dont hesitate to give a thumbs up for the answer in case it has helped you

1)

The p-value as per the ANOVA results is 0.6866

p-value of 0.6866 is greater than the alpha of 0.05.

So, we fail to reject the null hypothesis and conclude that p-value is greater than the significance level.

This is same as statement B

Answer: B. No​, because the​ P-value is greater than the significance level

2)

This means that the null hypohtesis that the mean weights are equal can't be rejected due to lack of evidence against the null hypothesis. Hence, the correct statement is C.

Answer: C. No​, because it is not likely that the candies do not have equal mean weights.