Question

Construct a 90​% confidence interval of the population proportion using the given information. x=40, n=200

The lower bound is?

The upper bound is?

(round to three decimal places as needed)

Answer 1

Solution :

Given that,

n = 200

x = 40

= x / n = 40/200 = 0.20

1 - = 1 - 0.2 = 0.80

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 * [(0.20 * 0.80) / 200]

= 0.047

A 90% confidence interval for population proportion p is ,

- E < P < + E

0.20 - 0.047 < p < 0.20 - 0.047

0.153 < p < 0.247