Question

A random sample of 400 CLU students is taken. 395 students reported that Econ 311 was their favorite class. Calculate the margin of error for a 96% confidence interval.

Answer 1

The margin of error for a 96% confidence interval is of 0.0114 = 1.14%.

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)`.

The margin of error is given by:

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

For this problem, we have that:

`n = 400, p = (395)/(400) = 0.9875`

96% confidence level

So
`\alpha = 0.04`, z is the value of Z that has a pvalue of
`1 - (0.04)/(2) = 0.98`, so
`Z = 2.056`.

Calculate the margin of error for a 96% confidence interval.

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

`M = 2.056\sqrt{(0.9875(0.0125))/(400)}`

`M = 0.0114`

The margin of error for a 96% confidence interval is of 0.0114 = 1.14%.