Question

onstruct a

9090​%

confidence interval of the population proportion using the given information.

x equals 75 comma n equals 250x=75, n=250

The lower bound is

nothing .

The upper bound is

nothing .

​(Round to three decimal places as​ needed.)

Answer 1

solution :

Given that,

n = 250

x = 75

= x / n = 75/250 = 0.3

1 - = 1 - 0.3 = 0.7

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 * (((0.3 * 0.7) / 250) = 0.048

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.3 - 0.048 < p < 0.3 + 0.048

0.252 < p < 0.348

The 90% confidence interval for the population proportion p is : ( 0.226 , 0.274)