Respuesta :
Answer:
[tex]z_{\alpha/2}=1.96[/tex]
And the margin of error would be:
[tex] ME = 1.96 \sqrt{\frac{0.63*(1-0.63)}{100} +\frac{0.472*(1-0.472)}{125}}= 0.1289[/tex]
And the best option would be:
± 0.1289
Step-by-step explanation:
We have the following info given from the problem
[tex] X_1 =63[/tex] represent the number urban residents in favor the construction
[tex]n_1 =100[/tex] represent the sample of urban residents
[tex]\hat p_1= \frac{63}{100}=0.63[/tex] estimated proportion of urban residents in favor the construction
[tex] X_2 =59[/tex] represent the number suburban residents in favor the construction
[tex]n_2 =125[/tex] represent the sample of surban residents
[tex]\hat p_2= \frac{59}{125}=0.472[/tex] estimated proportion of suburban residents in favor the construction
And for this case the confidence interval for the difference in the two proportions is given by:
[tex] (\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1 (1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
Since the confidence is 95% then the significance level is 5% and the critical value for this case using the normal standard distribution or excel is:
[tex]z_{\alpha/2}=1.96[/tex]
And the margin of error would be:
[tex] ME = 1.96 \sqrt{\frac{0.63*(1-0.63)}{100} +\frac{0.472*(1-0.472)}{125}}= 0.1289[/tex]
And the best option would be:
± 0.1289
