Question

Use the given level of confidence and sample data to construct a confidence interval for the population proportion p.

n= 195, p^=p hat= 0.831, Confidence level=95%

a.) 0.777

Answer 1

The 95% confidence interval for the population proportion is (0.778, 0.884).

Explanation:

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.831.

The standard error of the proportion is:

`\sigma_p=\sqrt{(p(1-p))/(n)}=\sqrt{(0.831*0.169)/(195)}\\\\\\ \sigma_p=√(0.00072)=0.027`

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

`MOE=z\cdot \sigma_p=1.96 \cdot 0.027=0.053`

Then, the lower and upper bounds of the confidence interval are:

`LL=p-z \cdot \sisgma_p = 0.831-0.053=0.778\\\\UL=p+z \cdot \sisgma_p = 0.831+0.053=0.884`

The 95% confidence interval for the population proportion is (0.778, 0.884).