Do teachers find their work rewarding and satisfying? The article presents the results of a survey of 399 primary school teachers and 264 senior teachers. Of the elementary school teachers, 223 said they were very satisfied with their jobs, whereas 127 of the high school teachers were very satisfied with their work. Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95%CI.(UsePelementary−Phigh school. Round your answers to four decimal places.)

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curwyrm · Accepted Answer

Step 1  Let Pelementary denotes the population proportion of all elementary school teachers who are satisfied, and Phigh school denotes the population proportion of all high school teachers who are satisfied. The test assertion is that there is a difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied. The hypothesis is,  Null hypothesis:  H0:Pelementary−Phigh school=0  Alternative hypothesis:  H1:Pelementary−Phigh school≠0  The sample proportion of all elementary school teatcher who are satisfied is,  P^elementary=x1n1  =223399  =0.5589  The sample proportion of all elementary school teachers who are satisfied is 0.5589.  The sample proportion of all high school teachers who are satisfied is,  P^high school=x1n1  =127264  =0.4811  The sample proportion of all high school teachers who are satisfied is 0.4811.  Step 2  Computation of critical value:  (1−α)=0.95  α=0.05  α2=0.025  1−α2=0.0975  The critical value of z-distribution can be obtained using the excel formula “=NORM.S.INV(0.975)&quot;. The critical value is 1.96.  The 95% confidence interval for the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied is, CI=P^elementary−P^high school±zα2P^elementary(1−P^elementary)nelementary+P^high school(1−P^high school)n(nhigh school)  =(0.5589−0.4811)±1.960.5589(1−0.5589)399+0.4811(1−0.4811)264  =0.0778±0.0775  =(0.0778−0.0775,0.0778+0.0775)  =(0.0003,0.1553)  Hence, the 95% confidence interval for the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied is (0.0003, 0.1553).  Decision rule:  If the confidence interval does not contains value zero, then reject the null hypothesis.  Conclusion:  The confidence interval does not contain a zero value.  Based on the decision rule, reject the null hypothesis.  Thus, there is difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied.

Do teachers find their work rewarding and satisfying? The article presents the results of a survey of 399 primary school teachers and 264 senior teach

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