Question

In a recent survey, a random sample of 130 families were asked about whether they have a pet, and 67 reported that they have a pet. What value of z should be used to calculate a confidence interval with a 90% confidence level

Answer 1

z = 1.645 should be used.

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)`.

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`.

z = 1.645 should be used.