Question

A survey of a random sample of virginia residents shows the following levels of satisfaction with their health care.

                                                                 satisfaction level

                                              low                    medium                       high

socio-economic class

lower                                 50                       30                            15

middle                               120                      70                            10

upper                                 10                      25                            60

Using SPSS, find γ and the related p-value. Is the satisfaction level independent of ses? How do you know?

Answer 1

Solution: We can use chi square test of indpendence to see if the satisfaction level is indpendent of socio economic class.

The null and alternative hypotheses are:

$H_{0}:$ Satisfaction level is independent of Socio-economic class

$H_{a}:$ Satisfaction level is not independent of Socio-economic class

Using the SPSS, we have below outputs:

Therefore, we have:

$\chi^{2}=138.853$

$p-value=0.000$

Since the $p-value=0.000$ is less than significance level (assuming $\alpha=0.05$ ), therefore, we reject the null hypothesis and conclude that satisfaction level is not independent of socio-economic class.