Question

The Paralyzed Veterans of America is a philanthropic organization that relies on contributions. They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution. To test a new campaign, they recently sent letters to a random sample of 100,000 potential donors and received 4781 donations. Give a 95% confidence interval for the true proportion of their entire mailing list who may donate.

Answer 1

Confidence interval: (0.04649,0.04913)

Explanation:

We are given the following in the question:

Sample size, n = 100,000

Number of people who donated, x = 4781

`\hat{p} = (x)/(n) = (4781)/(100000) = 0.04781`

95% Confidence interval:

`\hat{p}\pm z_(stat)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

Putting the values, we get:

`0.04781 \pm 1.96(\sqrt{(0.04781 (1-0.04781 ))/(100000)})\\\\=0.04781 \pm 0.00132\\\\=(0.04649,0.04913)`

is the required 95% confidence interval for the true proportion of their entire mailing list who may donate.