Question

(Aside from providing the results of the simulation or statistical tests, be sure to answer the questions – in bold.)

Do people who work for non-profit organizations differ from those who work at for-profit companies when it comes to personal job satisfaction? Separate random samples were collected by a polling agency to investigate the difference. Data collected from 422 employees at non-profit organizations revealed that 377 of them were “highly satisfied.” From the for-profit companies, 431 out of 518 employees reported the same level of satisfaction. Use the 2-Proportion Z-test. Include your null and alternative hypotheses.

Answer 1

Let p1 be the proportion of employees who are satisfied by working in non-profit organizations. p1 = 377/422 = 0.89

Let p2 be the proportion of employees who are satisfied by working in for-profit organizations. p2 = 431/518 = 0.83

We have to test if p1-p2 significantly differs.

Since the significance level is not given, we will take it 0.05

pooled proportion p = 377+431 / 422+518 = 0.86

Standard error SE(p1-p2) = = 0.0227

Now z = (p1-p2) / SE(p1-p2) = (0.89-0.83) / 0.0227 = 2.64

For z = 2.64, p value = 0.00829

Clearly p < 0.05, Hence we have strong evidence against null hypothesis. Hence we conclude that people who work for non-profit organizations differ from those who work at for-profit companies when it comes to personal job satisfaction.