Question

In a sample of 408 new websites registered on the Internet, 37 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: $(0.0628,\ 0.1186)$

Step-by-step explanation:

Given : Significance level : $\alpha:1-0.95=0.05$

Critical value : $z_{\alpha/2}=\pm1.96$

Sample size : n= 408

Proportion of new websites registered on the Internet were anonymous :

$\hat{p}=\dfrac{37}{408}\approx0.0907$

The formula to find the confidence interval for population proportion is given by :-

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

i.e. $0.0907\pm (1.96)\sqrt{\dfrac{0.0907(1-0.0907)}{408}}$

$=0.0907\pm0.0278665515649\\\\\approx 0.0907\pm0.0279\\\\=(0.0907-0.0279,\ 0.0907+0.0279)\\\\=(0.0628,\ 0.1186)$

Hence,  the 95 percent confidence interval for the proportion of all new websites that were anonymous = $(0.0628,\ 0.1186)$