Question

In: Statistics and Probability

(Aside from providing the results of the simulation or statistical tests, be sure to answer the...

(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.

Solutions

Expert Solution

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.


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