In an article in CA Magazine, Neil Fitzgerald surveyed Scottish business custome

Question

In an article in CA Magazine, Neil Fitzgerald surveyed Scottish business customers concerning their satisfaction with aspects of their banking relationships. Fitzgerald reports that, in 425 telephone interviews conducted by George Street Research, 71 percent of the respondents gave their banks a high rating for overall satisfaction.

(a) Assuming that the sample is randomly selected, calculate a 99 percent confidence interval for the proportion of all Scottish business customers who give their banks a high rating for overall satisfaction. (Round your answers to 3 decimal places.)

Explanation / Answer

Here n=425 and p=0.71

a. For 99% CI z value is 2.58 as from standard normal table P(-2.58<z<2.58)=0.99

Now Margin of Error=z*SE(p), Where SE(p)=sqrt(p(1-p)/n)

So SE(p)=sqrt(0.71*0.29/425)= 0.022

Hence E=0.022*2.58=0.057

Finlly CI=p+/-E=0.71+/-0.057=(0.653,0.767)

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.