Question

The sample survey showed that 72% of Internet users said the Internet has generally strengthened their relationship with family and friends. Develop a 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends.

Answer 1

The 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends is:

`0.72 \pm 1.96\sqrt{(0.72*0.28)/(n)}`

In which n is the sample size of the survey.

Explanation:

In a sample with a number n of people surveyed with a probability of a success of
`\pi`, and a confidence level of
`1-\alpha`, we have the following confidence interval of proportions.

`\pi \pm z\sqrt{(\pi(1-\pi))/(n)}`

In which

z is the z-score that has a p-value of
`1 - (\alpha)/(2)`.

The sample survey showed that 72% of Internet users said the Internet has generally strengthened their relationship with family and friends.

This means that
`\pi = 0.72`

95% confidence level

So
`\alpha = 0.05`, z is the value of Z that has a p-value of
`1 - (0.05)/(2) = 0.975`, so
`Z = 1.96`.

Confidence interval:

`\pi \pm z\sqrt{(\pi(1-\pi))/(n)}`

`0.72 \pm 1.96\sqrt{(0.72*0.28)/(n)}`

The 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends is:

`0.72 \pm 1.96\sqrt{(0.72*0.28)/(n)}`

In which n is the sample size of the survey.