Question

Construct a confidence interval of the population proportion at the given level of confidence. x = 125, n = 250, 90 % confidence.
The 90​% confidence interval is ____________?
​(Use ascending order. Round to three decimal places as​ needed.)

Answer 1

Answer: 90% confidence interval would be (0.448, 0.552).

Step-by-step explanation:

Since we have given that

x = 125

n = 250

So, $\hat{p}=\dfrac{x}{n}=\dfrac{125}{250}=0.5$

We need to find the 90% confidence interval.

so, z = 1.64

So, interval would be

$\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.5\pm 1.64\sqrt{\dfrac{0.5\times 0.5}{250}}\\\\=0.5\pm 0.0519\\\\=(0.5-0.0519,0.5+0.0519)\\\\=(0.448,0.552)$

Hence, 90% confidence interval would be (0.448, 0.552)