Answer to Question #134746 in Statistics and Probability for Margaret

Question

Suppose we take a sample of 200 Facebook profiles and found only 34 to be ghost profile.
What is the 95% CI for the proportion of Facebook ghost profile?
1. (0.1179 ; 0.2221)
2. (0.1169 ; 0.2231)
3. (0.1015 ; 0.2385)
4. (0.1263 ; 0.2137)
5. None of the above

Answer 1

We need to construct the 95% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X=34

Sample Size N=200

The sample proportion is computed as follows:

$\widehat{p}=\frac{X}{N}$ =$\frac{34}{200}=0.17$

Using Z table , the critical value for α=0.05 is 

$z_c = z_{1-\alpha/2} = 1.96$ The corresponding confidence interval is computed as shown below:

$\begin{array}{ccl} CI(\text{Proportion})= \displaystyle \left( \hat p - z_c \sqrt{\frac{\hat p (1-\hat p)}{n}}, \hat p + z_c \sqrt{\frac{\hat p (1-\hat p)}{n}} \right) \\\\= \displaystyle \left( 0.17 - 1.96 \times \sqrt{\frac{0.17 (1- 0.17)}{200}}, 0.17 + 1.96 \times \sqrt{\frac{0.17 (1- 0.17)}{200}} \right) \\ \\= (0.1179, 0.221) \end{array}$

Answer: option 1