Question

Construct a 90​% confidence interval of the population proportion using the given information. x equals 240 comma n equals 300 The lower bound is nothing. The upper bound is nothing. ​(Round to three decimal places as​ needed.)

Answer 1

Solution :

Given that,

n = 300

x = 240

= x / n = 240 / 300 = 0.8

1 - = 1 - 0.8 = 0.2

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 * (((0.8 * 0.2) / 300) = 0.038

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.8 - 0.038 < p < 0.8 + 0.038

0.762 < p < 0.838

The 90% confidence interval for the population proportion p is : ( 0.762 , 0.838)