Question

Chauncey determined that 50 percent of students at his school voted Republican in the last election, with a sampling error (also known as standard error) of 5 percent. What is the confidence interval for 95 percent confidence level?

Answer 1

95% confidence interval: (0.402,0.598)

Explanation:

We are given the following in the question:

Proportion of student who voted Republican in the last election = 50%

`\hat{p} = 50\% = 0.5`

Standard error = 5% = 0.05

95% confidence interval:

`\hat{p}\pm z_(stat)* (\text{Standard error})`

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

Putting values, we get,

`=0.5 \pm (1.96)(0.05)\\=0.5\pm 0.098\\=(0.402,0.598)`

is the required confidence interval.