Answer to Question #275493 in Statistics and Probability for Cleo

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.