Answer: A. As the sample size is appropriately large , the margin of error is [tex]\pm0.171[/tex].
Step-by-step explanation:
Given : The sample size : n=30, it means the sample is large , so we apply z-test. [If n ≥ 30 then we apply z-test]
The proportion of customers surveyed were satisfied with the service offered : [tex]\hat{p}=0.65[/tex]
Significance level : [tex]\alpha: 1-0.95=0.05\\[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
Margin of error :-
[tex]E=\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
i.e. [tex]E= \pm(1.96)\sqrt{\dfrac{0.65(1-0.65)}{30}}=\pm0.171[/tex]
