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

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 450 telephone interviews conducted by George Street Research, 53 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?

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 450 telephone interviews conducted by George Street Research, 53 percent of the respondents gave their banks a high rating for overall satisfaction.

Explanation / Answer

p^ = 0.53

n = 450

99% -Z0.005 = 2.575

sqrt(p^*q^/n) = sqrt(0.53*0.47/450) = 0.0235277614

(0.53 - 2.575 *0.0235277614 , 0.53 + 2.575 *0.0235277614)

=(0.4694, 0.59058)

b) since each value of confidenc e interval is less than 0.60 (60 %)

we can not be 99 percent confident that more than 60 percent of all Scottish business customers give their banks a high rating for overall satisfaction.

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