Question

Construct a confidence interval of the population proportion at the given level of confidence. x =75, n = 150 , 90 % confidence.

Answer 1

Solution :

Given that,

n = 150

x = 75

Point estimate = sample proportion = = x / n = 75 / 150 = 0.500

1 - = 1 - 0.500 = 0.500

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)

= 1.96 * (((0.500 * 0.500) / 150)

= 0.067

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.500 - 0.067 < p < 0.500 + 0.067

0.433 < p < 0.567

The 95% confidence interval for the population proportion p is : (0.433 , 0.567)