Chapter 12, Problem 1CQQ

Cola Weights Data Set 26 “Cola Weights and Volumes” 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 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 equality of the mean weights from the four samples?

To determine

To obtain: The null hypothesis for the analysis of variance test.

To explain: The conclusion about $H_0$.

To conclude: The equality of mean weights from the four samples.

Answer to Problem 1CQQ

The null hypothesis is $H_0:{\mu }_1={\mu }_2={\mu }_3={\mu }_4$.

The conclusion about $H_0$ is that there is sufficient evidence to reject the claim that the mean weights of the contents of cans of cola from four different samples are the same.

No, the equality of mean weights from the four samples cannot be concluded.

Explanation of Solution

Given info:

The data shows that the weights of the contents of cans of cola from four different samples.

Calculation:

State the test hypotheses.

Let ${\mu }_1$ be the mean weight of regular Coke, ${\mu }_2$ be the mean weight of diet Coke and ${\mu }_3$ be the mean weights of regular Pepsi and ${\mu }_4$ be the mean weights of diet Pepsi.

Null hypothesis:

$H_0:{\mu }_1={\mu }_2={\mu }_3={\mu }_4$

Alternative hypothesis:

$H_1:$ At least one of the means is different from the other means

From the Minitab output,

The test statistic F is 503.06 and the P-value is 0.000.

Decision criteria for the P-value method:

If $P\text{-value}\le \alpha \text{,}$ then reject the null hypothesis $\left(H_0\right)$.

If $P\text{-value}>\alpha \text{,}$ then fail to reject the null hypothesis $\left(H_0\right)$.

Conclusion:

The P-value is 0.000 and the significance level is 0.05.

Here, the P-value is lesser than the significance level.

That is, $0.000\left(=P\text{-value}\right)<0.05\left(=\alpha \right)$.

Here, the null hypothesis is rejected.

Thus, there is sufficient evidence to reject the claim that the mean weights of the contents of cans of cola for four different samples are same.

Justification:

No, the equality of mean weights from the four samples cannot be concluded because the mean weights of the contents of cans of cola from four different samples are different