Question

In a sample of 679 new websites registered on the Internet, 42 were anonymous (i.e., they shielded their name and contact information). (a) Construct a 95 percent confidence interval for the proportion of all new websites that were anonymous. (Round your answers to 4 decimal places.)

Answer 1

Answer:

95% Confidence interval:  (0.0429,0.0791)      

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 679

Number of anonymous websites, x = 42

$\hat{p} = \dfrac{x}{n} = \dfrac{42}{679} = 0.0618$

95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96$

Putting the values, we get:

$0.0618\pm 1.96(\sqrt{\dfrac{0.0618(1-0.0618)}{679}}) = 0.0618\pm 0.0181\\\\=(0.0429,0.0791)$

is the required confidence interval for proportion of all new websites that were anonymous.