05 level of significance Step 1 1 2 3 4 5 1 ℎ 1 Did not complete high school 2

05 level of significance step 1 1 2 3 4 5 1 ℎ 1 did

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educations at 0.05 level of significance? Step 1) 𝐻 0 : 𝜇 1 = 𝜇 2 = 𝜇 3 = 𝜇 4 = 𝜇 5 𝐻 1 : 𝑁?? 𝑎?? ?ℎ𝑒 ?𝑒𝑎?? 𝑎?𝑒 𝑒??𝑎? 1 = Did not complete high school 2 = High school degree 3 = Some college 4 = College degree 5 = Post-undergraduate degree Step 2) Find the mean for each group Analyze > Compare Means > Means… Step 3) In the ANOVA table, the p-value = 0.000 < 0.05 We reject the null hypothesis. We conclude that there is a significant difference in the mean Household income among the 5 level of educations. Report Household income in thousands Level of education Mean N Std. Deviation Did not complete high school 59.8662 1390 61.30036 High school degree 66.2071 1936 72.72591 Some college 70.1346 1360 81.03878 College degree 78.6502 1355 92.87753 Post-undergraduate degree 87.1699 359 94.79998 Total 69.4748 6400 78.71856 ANOVA Household income in thousands Sum of Squares df Mean Square F Sig. Between Groups 376079.699 4 94019.925 15.309 .000 Within Groups 39276042.251 6395 6141.680 Total 39652121.950 6399
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17 Step 4) Multiple Comparisons Dependent Variable: Household income in thousands Tukey HSD (I) Level of education (J) Level of education Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound Did not complete high school High school degree -6.34094 2.75515 .144 -13.8585 1.1766 Some college -10.26837 * 2.98905 .005 -18.4242 -2.1126 College degree -18.78400 * 2.99184 .000 -26.9474 -10.6206 Post-undergraduate degree -27.30373 * 4.63964 .000 -39.9632 -14.6442 High school degree Did not complete high school 6.34094 2.75515 .144 -1.1766 13.8585 Some college -3.92743 2.77278 .617 -11.4931 3.6382 College degree -12.44306 * 2.77578 .000 -20.0169 -4.8692 Post-undergraduate degree -20.96279 * 4.50334 .000 -33.2504 -8.6752 Some college Did not complete high school 10.26837 * 2.98905 .005 2.1126 18.4242 High school degree 3.92743 2.77278 .617 -3.6382 11.4931 College degree -8.51563 * 3.00808 .038 -16.7233 -.3079 Post-undergraduate degree -17.03536 * 4.65013 .002 -29.7235 -4.3472 College degree Did not complete high school 18.78400 * 2.99184 .000 10.6206 26.9474 High school degree 12.44306 * 2.77578 .000 4.8692 20.0169 Some college 8.51563 * 3.00808 .038 .3079 16.7233 Post-undergraduate degree -8.51973 4.65192 .355 -21.2127 4.1733 Post-undergraduate degree Did not complete high school 27.30373 * 4.63964 .000 14.6442 39.9632 High school degree 20.96279 * 4.50334 .000 8.6752 33.2504 Some college 17.03536 * 4.65013 .002 4.3472 29.7235 College degree 8.51973 4.65192 .355 -4.1733 21.2127 *. The mean difference is significant at the 0.05 level. In Did not complete high school & High school degree, the hypothesis is 𝐻 0 : 𝜇 1 = 𝜇 2 𝐻 1 : 𝜇 1 ≠ 𝜇 2 The mean difference = -6.34. P-value = 0.144 > 0.05 In High school degree & Some college, the hypothesis is 𝐻 0 : 𝜇 2 = 𝜇 3 𝐻 1 : 𝜇 2 ≠ 𝜇 3
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18 The mean difference = -3.93. P-value = 0.617 > 0.05 In College degree & Post-undergraduate degree, the hypothesis is 𝐻 0 : 𝜇 4 = 𝜇 5 𝐻 1 : 𝜇 4 ≠ 𝜇 5 The mean difference = -8.52. P-value = 0.355 > 0.05 We do not reject the above null hypothesises. We do not have evidences to conclude that there are significant differences between the means of Did not complete high school & High school degree, High school degree & Some college, College degree & Post-undergraduate degree. All other p-values< 0.05. We reject these null hypotheses. We have enough evidence to conclude that there are significant differences between Did not complete high school and Some College, between Did not complete high school and College degree, between Did not complete high school and Post-undergraduate degree, High school degree and College degree, High school degree and Post-undergraduate degree, Some college and College degree, Some college and Post- undergraduate degree.
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