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 4573 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?

Answer 1

a)

Sample proportion = 4573 / 100000 = 0.046

90% confidence interval for p is

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

0.046 - 1.645 * sqrt [ 0.046 * ( 1 - 0.046) / 100000] < p < 0.046 + 1.645 * sqrt [ 0.046 * ( 1 - 0.046) / 100000]

0.045 < p < 0.047

90% CI is ( 0.045 , 0.047 )

b)

Since 0.049 is not contained in confidence interval, the rate is not plausible.