Answer to Question #113727 in Statistics and Probability for Katenda

Question

Suppose we take a sample of 200 Facebook profiles and found only 34 to be ghost profiles. Use this information to answer questions 7 and 8.

Question 7

What is the 95% CI for the proportion of Facebook ghost profile?

(1) (0.1263; 0.2137)
(2) (0.1169; 0.2231)
(3) (0.1015; 0.2385)
(4) (0.1263; 0.2137)
(5) None of the above.


Question 8

What is the upper limit for the 99% confidence interval estimate of the proportion of Facebook ghost profiles?

(1) 0.2137
(2) 0.1015
(3) 0.2137
(4) 0.2385
(5) 0.2231

Answer 1

$Question\; 7\\ Let\;\hat p=\frac{34}{200}=0.17\\ Then,\; \text{the confidence interval for the proportion }\\ \text{can be calculated as follows:}\\ \hat p±Z_{\frac{α}{2}}(\sqrt{\frac{\hat p(1-\hat p)}{n}}),\\ \hat p=0.17\\ Z_{\frac{α}{2}}=Z_{\frac{0.05}{2}}=Z_{0.025}=1.96,\\ n=200\\ \text{ the lower limit }= 0.17-1.96(\sqrt{\frac{0.17(1-0.17)}{200}})\\ =0.1179\\ \text{ the upper limit} = 0.17+1.96(\sqrt{\frac{0.17(1-0.17)}{200}})\\ =0.2221\\ \text{the answer is (5) none of the above}\\ Question \;8\\ Z_{\frac{α}{2}}=Z_{\frac{0.01}{2}}=Z_{0.005}=2.58,\\ \text{ the upper limit} = 0.17+2.58(\sqrt{\frac{0.17(1-0.17)}{200}})\\ =0.2385\\ \text{the answer is (4) 0.2385}\\$