Chapter 12, Problem 1CQQ

To determine

Identify the null hypothesis for the given analysis of variance test and state the conclusion about $H_0$. Also, state the conclusion about 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 “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

Calculation:

Define the variable:

${\mu }_1$: Mean weight of regular Coke

${\mu }_2$:Mean weight of diet Coke

${\mu }_3$: Mean weights of regular Pepsi

${\mu }_4$: Mean weights of diet Pepsi

The hypotheses are given below:

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 EXCEL output, the test statistic F is 503.0618 and the P-value is 0.000.

Condition:

If P-value is less than the level of significance, then reject the null hypothesis.

Conclusion:

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

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

Hence, 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. This result suggests that the equality of mean weights from the four samples cannot be concluded.