In an article in CA Magazine Neil Fitzgerald surveyed Scotti

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 424 telephone interviews conducted by George Street Research, 51 percent of the respondents gave their banks a high rating for overall satisfaction.

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.)

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?

Solution

a) p = 0.51...n = 424...
lower limit = 0.51 - (2.58* sqrt(0.49*0.51 / 424) = 0.447.....
upper limit = 0.51+ (2.58* sqrt(0.49*0.51 / 424)= 0.573......interval = [ 0.447 , 0.573 ].....

b) See the interval is below 0.6...so, at 99% confidence, we can NOT say that more than 60 percent of all Scottish business customers give their banks a high rating for overall satisfaction....