Question

The Pew Research Center Internet Project conducted a survey of 957 Internet users. This survey provided a variety of statistics on them. If required, round your answers to four decimal places. (a) The sample survey showed that 90% 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.

Answer 1

Answer: (0.881, 0.919)

Step-by-step explanation:

Let p be the population proportion of respondents who say the Internet has been a good thing for them personally.

Confidence interval for population proportion is given by :-

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$ , where z* = Critical value ,

$\hat{p}$ = Sample proportion

n = sample size.

As per given , we have

n= 957

$\hat{p}=0.90$

By z-table , Critical value for 95% confidence interval : z*= 1.96

Then, the 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. will be :

$0.90\pm 1.96\sqrt{\dfrac{0.90(1-0.90)}{957}}$

$0.90\pm 1.96\sqrt{0.0000940438871473}$

$0.90\pm 1.96(0.00969762275753)$

$\approx0.90\pm 0.019\\\\=(0.90-0.019,\ 0.90+0.019)$

$(0.881,\ 0.919)$

Hence, the required 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally = (0.881, 0.919)