Question

Construct a 95% confidence interval of the population proportion using the given information. (Please answer parts a. and b.) x= 90 n=300

Answer 1

Solution :

Given that,

a) Point estimate = sample proportion = = x / n = 90 / 300 = 0.30

1 - = 1 - 0.30 = 0.70

b) Z/2 = Z_0.025 = 1.96  

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

= 1.96 (((0.30 * 0.70) / 300 )

= 0.052

A 95% confidence interval for population proportion p is ,

± E   

= 0.30  ± 0.052

= ( 0.248, 0.352 )