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)`

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}=(37)/(408)\approx0.0907`

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

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

i.e.
`0.0907\pm (1.96)\sqrt{(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)`