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

Answer:

95% confidence interval: (0.402,0.598)

Step-by-step 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:

$\hat{p}\pm z_{stat}\times (\text{Standard error})$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

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.