In an article in CA Magazine , Neil Fitzgerald surveyed Scottish business custom
ID: 3132294 • Letter: I
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 446 telephone interviews conducted by George Street Research, 77 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 446 telephone interviews conducted by George Street Research, 77 percent of the respondents gave their banks a high rating for overall satisfaction.
Explanation / Answer
A)
Note that
p^ = point estimate of the population proportion = x / n = 0.77
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.019926997
Now, for the critical z,
alpha/2 = 0.005
Thus, z(alpha/2) = 2.575829304
Thus,
Margin of error = z(alpha/2)*sp = 0.051328542
lower bound = p^ - z(alpha/2) * sp = 0.718671458
upper bound = p^ + z(alpha/2) * sp = 0.821328542
Thus, the confidence interval is
( 0.718671458 , 0.821328542 ) [ANSWER]
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b)
As we can see, this whole interval is above 0.6.
YES, the interval is ABOVE 0.6. [ANSWER]
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