5. In the HSB data set, compare the means for private and public school students on the self~concept measure, i.e., test the null hypothesis that the mean of the population of selfsconcept scores for private school students is the same as the mean for the public school students (use or = .01). Report the values of K and 172, the standard errors of these two means, 3,71 and 3,72, the sample sizes ml and tag, the 1value of the test statistic, t, and the pvalue associated with this value of t. Clearlyr state your decision regarding the null hypothesis and your conclusion in the context of the problem. The TTEST Procedure Variable: CONCPT SCTYP Method N Mean Std Dev Std Err Minimum Maximum 1- Public School 506 -0.00470 0.7053 0.0314 -2.6200 1.1900 2- Private School 94 0.0567 0.7082 0.0730 -2.6000 1.1900 Diff (1-2) Pooled 0.0614 0.7057 0.0793 Diff (1-2) Satterthwaite 0.0614 0.0795 SCTYP Method Mean 95% CL Mean Std Dev 95% CL Std Dev 1- Public School -0.00470 -0.0663 0.0569 0.7053 0.6644 0.7517 2- Private school 0.0567 -0.0883 0.2018 0.7082 0.6194 0.8269 Diff (1-2) Pooled -0.0614 -0.2171 0.0943 0.7057 0.6679 0.7482 Diff (1-2) Satterthwaite -0.0614 -0.2187 0.0959 Method Variances DF t Value Pr > |t| Pooled Equal 598 -0.77 0.4388 Satterthwaite Unequal 129.62 -0.77 0.4412 Equality of Variances Num Den Method DF DF F Value Pr > F Folded F 93 505 1.01 0.9299