A philanthropic organisation sent free mailing labels and greeting cards to a ra

Question

A philanthropic organisation sent free mailing labels and greeting cards to a random sample of 100,000 potential donors on their mailing list and received 4956 donations. (a) Give a 90% confidence interval for the true proportion of those from their entire mailing list who may donate. (b) A staff member thinks that the true rate is 4.9%. Given the confidence interval you found, do you find that rate plausible? (a) What is the 90% confidence interval? The 90% confidence interval is from % to %. (Round to two decimal places as needed.) (b) Given the confidence interval you found, is the proposed true rate, 4.9%, plausible? Yes No

Explanation / Answer

Solution:-

Standard error of the mean = SEM = x(N-x)/N3 = 0.001

= (1-CL)/2 = 0.050

Standard normal deviate for = Z = 1.645

Proportion of positive results = P = x/N = 0.050

Lower bound = P - (Z*SEM) = 0.048

Upper bound = P + (Z*SEM) = 0.051

90% confidence interval is from 4.8% to 5.1%.

Yes, as it falls in the confidence interval.

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