A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected from each group. Their ages are recorded below. Test the claim that at least one mean is different from the others. Use α = 0.01. ### Teacher Age Data#### Elementary School Teachers- 23- 28- 27- 25- 52- 37#### High School Teachers- 41- 36- 38- 47- 42- 31#### Community College Teachers- 39- 45- 36- 61- 45- 35This table presents the ages of teachers at different educational levels: Elementary School, High School, and Community College. Each column lists the ages of individual teachers within each group.

Name: A researcher wishes to determine whether there is a difference in the
Uploaded: 2024-03-20T07:06:16.000Z
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Description: A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected from each group. Their ages are recorded below. Test the claim that at

The data for ages of elementary school, high school, and community college teachers is as given in the following table, Elementary School teachers High School teachers Community College Teachers 23 41 39 28 36 45 27 38 36 25 47 61 52 42 45 37 31 35 It is required to test whether there is a difference in the average age of the elementary school, high school, and community college teachers. The given level of significance is 0.01Null and alternative hypothesis: To test the given claim the hypothesis is given as H0: There is no difference in the average age of elementary school, high school, and community college teachers. H1: At least one average is different than others. The level of significance: From the given, the level of significance is (α) =0.01. Test statistic and P-value (Since there are three groups, we have to use the one-way ANOVA) It can be solved using MS-Excel. Steps for solving using MS-Excel are as follows Enter the data in MS-Excel Click on the Data toolbar >> Select the Data Analysis >> ANOVA: Single Factor. Select the entire data as an input range. (Check labels if included) Enter the desired level of significance. Here it is 0.01. Press ok The output obtained is as follows From the above : The test statistic (F) is given as F = 2.516579 The P-value = 0.114173 P-value decision rule: Since P-value ( 0.114173) is greater than the level of significance (0.01), we failed to reject the H0. Conclusion: Hence, there is sufficient evidence to conclude that there is no difference in the average age of elementary school, high school, and community college teachers.