Question

Does number of goof friends depend on happiness? 

(GSS Data)

Very happy                Pretty happy                         Not too happy

Mean              10.4                                        7.4                                          8.3                  

 

Std. dev.        17.8                                        13.6                                        15.6

 

N                    27.6                                        468                                         87

 

 

                                   Sum of                       Mean

 

Source                       squares         df        square           F         Sig

 

Between-groups      1627               2         813                 3.47    0.032

 

Within-groups          193901           828     234

 

Total                          195528           830

Answer 1

The hypotheses tested are,

$H_0:$ Number of good friends depend on happiness

$Against$

$H_1:$ Number of good friends does not depend on happiness

We are going to use the given ANOVA table results to make a decision.

From the ANOVA table, the test statistic is $F=3.47$ and the p-value $p(F\gt 3.47 )=0.032$.

The p-value is compared with the desired significance level of $\alpha=0.05$ and the null hypothesis is rejected if $p -value\lt \alpha.$

Since $p-value=0.032\lt \alpha=0.05,$ we reject the null hypothesis and conclude that there is insufficient evidence to show that the number of friends depend on happiness at 5% level of significance.