Question

If n = 320 and ˆp (p-hat) = 0.35, construct a 90% confidence interval.Give your answers to three decimals

Answer 1

Explanation:

Given:

`n=320,\hat{p}=0.35`

We want to construct a 90% confidence interval.

The confidence interval for a population proportion is calculated using the formula:

`\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

For a 90% confidence , the critical value, z=1.645.

Substitute these values into the formula given:

`0.35\pm1.645\sqrt{(0.35(1-0.35))/(320)}`

We then simplify:

`\begin{gathered} \text{ Confidence Interval=}0.35\pm0.044 \\ =(0.35-0.044,0.35+0.044) \\ =(0.306,0.394) \end{gathered}`

The confidence interval (at 90%) is (0.306, 0