Question

a major metroplitan newspaper selected a simple random sample of 1,600 readers from their list of 100,000 subscribers. they asked wether the paper should increase its coverage of local news. forty percent of the sample wanted mre local news. WHat is the 99% confidence interval for the proportion of readers who would like more coverage of local news

Answer 1

The 99% confidence interval for the proportion of readers who would like more coverage of local news is (0.3685, 0.4315).

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 zscore that has a pvalue of
`1 - (\alpha)/(2)`.

For this problem, we have that:

`n = 1600, \pi = 0.4`

99% confidence level

So
`\alpha = 0.01`, z is the value of Z that has a pvalue of
`1 - (0.01)/(2) = 0.995`, so
`Z = 2.575`.

The lower limit of this interval is:

`\pi - z\sqrt{(\pi(1-\pi))/(n)} = 0.4 - 2.575\sqrt{(0.4*0.6)/(1600)} = 0.3685`

The upper limit of this interval is:

`\pi + z\sqrt{(\pi(1-\pi))/(n)} = 0.4 + 2.575\sqrt{(0.4*0.6)/(1600)} = 0.4315`

The 99% confidence interval for the proportion of readers who would like more coverage of local news is (0.3685, 0.4315).