Answer:
a) p-hat = 0.428
b) Error = 0.026
c) 0.402 ≤ p ≤ 0.454
Step-by-step explanation:
We have a survey that was emailed to 2397 subjects and only 1025 were returned.
a) The best point estimate for p is p-hat=x/n:
[tex]\hat{p}=X/n=1025/2397=0.428[/tex]
b) The margin of error is the product of the z-score for a 99% interval and the standard deviation of the proportion.
The z-score for a 99% CI is z=2.576.
The standard deviation is:
[tex]\sigma=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\sqrt{\frac{0.428*0.572}{2397}}=0.010[/tex]
Then, the margin of error is:
[tex]E=z*\sigma=2.576*0.01=0.02576[/tex]
c) the confidence interval can be constructed as:
[tex]\hat{p}-z\sigma\leq p \leq \hat{p}-z\sigma\\\\0.428-0.026\leq p \leq 0.428+0.026\\\\ 0.402\leq p \leq0.454[/tex]