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.

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