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# Hypothesis Testing for Four Population Means with ANOVA Tables

1. Test to see if four population means are the same or different. Assume the populations are normally distributed and have equal variances. Use the formal hypothesis-testing model. State the conclusion in statistical terms and in conversational English. Use the ANOVA table below.

ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 900 3 300 3.00 0.0480
Within Groups 2500 25 100

Total 3300

2. ) I want to prove that a population mean is not 150. Use an alpha of 5% and set up the full, detailed, five step hypothesis test. Assume when the sample 200 is taken the sample standard deviation is 10 and the sample mean is 151.77. What is the p value?

#### Solution Preview

1. Test to see if four population means are the same or different. Assume the populations are normally distributed and have equal variances. Use the formal hypothesis-testing model. State the conclusion in statistical terms and in conversational English. Use the ANOVA table below.

ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 900 3 300 3.00 0.0480
Within Groups 2500 25 100

Total 3300

The null hypothesis in this test is that the means of the four populations are all the same. The alternative hypothesis is that at least one of the four means differs from the others.

The test statistic is shown under the column labeled "F". The value of the test statistic is F = 3.00. If the null hypothesis is true, this value is a randomly ...

#### Solution Summary

The hypothesis testing for four population means using ANOVA tables is determined.

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