Question

A research center project involved a survey of 846 internet users. It provided a variety of statistics on internet users. (a) The sample survey showed that 91% of respondents said the internet has been a good thing for them personally. Develop a 95% confidence interval for the proportion of respondents who say the internet has been a good thing for them personally. (Round your answers to four decimal places.)

Answer 1

95% Confidence interval: (0.8907,0.9293)

Explanation:

We are given the following in the question:

Sample size, n = 846

Proportion of respondents who said the internet has been a good thing for them personally = 91%

`\hat{p} = 0.91`

95% Confidence interval:

`\hat{p}\pm z_(stat)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

Putting the values, we get:

`0.91\pm 1.96(\sqrt{(0.91(1-0.91))/(846)})\\\\ = 0.91\pm 0.0193\\\\=(0.8907,0.9293)`

(0.8907,0.9293) is the required 95% confidence interval for the proportion of respondents who say the internet has been a good thing for them personally.