In a survey regarding job satisfaction, 574 in a sample of 934 female job-holders stated that they are satisfied with their jobs, while 500 in a sample of 755 male job-holders stated that they are satisfied with their jobs. the null hypothesis is that the proportions of all female and male job-holders who are satisfied with their jobs are the same. the alternative hypothesis is that the proportion of female job-holders who are satisfied with their jobs is lower than the proportion of male job-holders stated who are satisfied with their jobs. the significance level is 2.5%. what is the critical value of z for the hypothesis test?

If the critical value is the only thing of interest, then this question is quite easy. Referencing a z table, you look up the percentage of interest: in this case, we must be 97.5% certain in order to accept the null hypothesis (significance level =2.5%. The number that corresponds to .9750 on the z table is 1.96. This is our critical value.

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