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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?

User Buck Hicks
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1 Answer

4 votes

Answer:

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.

User GazB
by
8.2k points
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