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ehidna [41]
3 years ago
9

In a sample of 408 new websites registered on the Internet, 37 were anonymous (i.e., they shielded their name and contact inform

ation). (a) Construct a 95 percent confidence interval for the proportion of all new websites that were anonymous. (Round your answers to 4 decimal places.)
Mathematics
1 answer:
xeze [42]3 years ago
8 0

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)

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