Given below are the analysis of variance results from a Minitab display. Assume

Question

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Source DF SS MS F p Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80 What can you conclude about the equality of the population means? A) Reject the null hypothesis since the p-value is greater than the significance level. We conclude that at least two of the factor means differ. B) Do not reject the null hypothesis since the p-value is greater than the significance level. We conclude that the factor means are equal. C) Reject the null hypothesis since the p-value is greater than the significance level. We conclude that all of the factor means differ. D) No conclusion can be made. E) Do not reject the null hypothesis since the p-value is greater than the significance level. There is not enough evidence to show that the factor means are unequal.

Explanation / Answer

Fail to reject the null hypothesis since the p-value is greater than the significance level. Accept the null hypothesis since the p-value is greater than the significance level Hence C is the correct option.

Take a decision based on the critical region or p-value

Explaining with an example

• Using the critical region: because the test statistics (z= 5.164) is greater that the critical value (z0.025=1.96) we reject the

null hypothesis.

• Using the p-value: because the p-value (0.0001) is lower than

the significance level (0.05) we reject the null hypothesis.

How to Set the Null and Alternative Hypotheses (example)
• Set the Null and Alternative Hypotheses about p (Proportion of adults that use alcohol beverages)
• Claim: p>0.5
• Since the claim does not contain the equal sign the claim becomes the Alternative Hypothesis.
• The opposite to the original claim is: p0.5. Since the opposite to the original claim contains the equal sign, this
becomes the Null hypothesis.
• Finally set the Null hypothesis to p=0.5
• We finally want to prove:
H0: p=0.5 vs. H1: p>0.5
• From the sign of the Alternative Hypothesis we figure out that we have a Right-Tailed test.

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