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 444 telephone interviews conducted by George Street Research, 50 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.) The 99 percent confidence interval is [ , ]. (b) Based on this interval, can we be 99 percent confident that more than 60 percent of all Scottish business customers give their banks a high rating for overall satisfaction? , the interval is 0.60.

Answer 1

a)

99% confidence interval for p is

- Z/2 * sqtr [ ( 1 - ) / n ] < p < + Z/2 * sqtr [ ( 1 - ) / n ]

0.50 - 2.576 * sqrt [ 0.50 * 0.50 / 444 ] < p < 0.50 + 2.576 * sqrt [ 0.50 * 0.50 / 444 ]

0.439 < p < 0.561

99% CI is ( 0.439 , 0.561 )

b)

Since all values in confidence interval are less than 0.60, we have sufficient evidence to say that

more than 60 percent of all Scottish business customers give their banks a high rating for overall satisfaction