Question

A survey reported that 70% of those responding to a national survey of college freshmen were interested in taking summer courses. Using the sample size of 49, calculate a 95% confidence interval for the proportion of college students who are interested in taking summer courses.

Answer 1

95% confidence interval: (0.5717,0.8283)

Explanation:

We are given the following in the question:

Sample size, n = 49

p = 70% = 0.7

Alpha, α = 0.05

The confidence interval can be calculated as:

`p \pm z_(critical)\sqrt{(p(1-p))/(n)}`

Putting the values, we get,

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

`0.7 \pm 1.96(\sqrt{(0.7(1-0.7))/(49)} ) = 0.7 \pm 0.1283 =(0.5717,0.8283)`

95% confidence interval: (0.5717,0.8283)