Q1CQQ Cola Weights Data Set 26 鈥楥ola... [FREE SOLUTION]

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Chapter 12: Q1CQQ (page 566)

Cola Weights Data Set 26 鈥楥ola Weights and Volumes鈥� in Appendix B lists the weights (lb) of the contents of cans of cola from four different samples: (1) regular Coke, (2) diet Coke, (3) regular Pepsi, and (4) diet Pepsi. The results from the analysis of variance are shown on the top of the next page. What is the null hypothesis for this analysis of variance test? Based on the displayed results, what should you conclude about H0? What do you conclude about the equality of the mean weights of the four samples?

Short Answer

Expert verified

The null hypothesis for the given test is

\({H_0}:{\mu _1} = {\mu _2} = {\mu _3} = {\mu _4}\).

There is no difference in the mean weights of the contents of the four sample cola.

As the p-value equal to 0.000 is very small, it can be said that the null hypothesis is rejected.

Thus, there is enough evidence to conclude that there is a significant difference in the mean weights of the four samples.

Step by step solution

Given information

The ANOVA table is provided for the sample mean weights considering the contents of four different samples of cola, which are (1) regular Coke, (2) diet Coke, (3) regular Pepsi, and (4) diet Pepsi.

Identify the null hypothesis

The null hypothesis is the 鈥榥o difference鈥� hypothesis that is paired with the alternative hypothesis under any hypothesis test.

In the comparison of more than two means, the one-way analysis of variance test is conducted as there is a single factor in consideration.

The null hypothesis that is constructed is

\({H_0}:{\mu _1} = {\mu _2} = {\mu _3} = {\mu _4}\).

Here,\({\mu _i}\)is the true mean weight of contents of the four samples of cola content.

That is, the null hypothesis states that there is no difference in the mean weights of the four samples.

State the decision rule

The p-value is compared to the level of significance to make a decision.

Assume that the significance level is 0.05.

As the p-value corresponding to the F-statistic value (under factor) of 503.06 is equal to 0.000, which is extremely small, the null hypothesis is rejected.

State the conclusion

As the null hypothesis is rejected, there is evidence to conclude that there is a significant difference in the mean weights of the four samples of cola content at the significance level of 0.05.