Question

The poll found that 38% of a random sample of 1012 American adults said they believe in ghosts. What is the lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts?

Answer 1

The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549

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 = 1012, \pi = 0.38`

90% confidence level

So
`\alpha = 0.1`, z is the value of Z that has a pvalue of
`1 - (0.1)/(2) = 0.95`, so
`Z = 1.645`.

The lower limit of this interval is:

`\pi - z\sqrt{(\pi(1-\pi))/(n)} = 0.38 - 1.645\sqrt{(0.38*0.62)/(1012)} = 0.3549`

The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549