Answer:
a) 99% Confidence interval: (0.045311,0.04875)
b) 4.7% is a plausible rate.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 100,000
Number of people who donated, x = 4703
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{4703}{100000} = 0.04703[/tex]
a) 99% Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.01} = 2.58[/tex]
Putting the values, we get:
[tex]0.04703\pm 2.58(\sqrt{\dfrac{0.04703(1-0.04703)}{100000}})\\\\= 0.04703\pm 0.00172\\\\=(0.04531,0.04875)[/tex]
b) A staff member thinks that the true rate is 4.74.7%.
Yes, this is a plausible rate as this value of 0.0474 lies in the calculated confidence interval as:
[tex]4.531\%<4.7\%<4.875\%[/tex]
