Question

A county clerk wants to estimate the proportion of voters who will need special election facilities.

Suppose a sample of 400 voters was taken.
If 150 need special election facilities, what is the upper confidence limit (UCL) for the 90% confidence interval for the population proportion of voters who will need special election facilities?
Round your answer to 3 decimal places.

Answer 1

Answer: The upper confidence limit for the 90% confidence interval would be 0.415.

Explanation:

Since we have given that

n = 400

x = 150

So,
`\hat{p}=(x)/(n)=(150)/(400)=0.375`

At 90% confidence interval, z = 1.645

So, margin of error would be

`z* \sqrt{(p(1-p))/(n)}\\\\=1.645* \sqrt{(0.375* 0.625)/(400)}\\\\=0.0398`

So, the upper limit would be

`\hat{p}+0.0398\\\\=0.375+0.0398\\\\=0.415`

Hence, the upper confidence limit for the 90% confidence interval would be 0.415.