Question

Construct a 95% confidence interval of the population proportion using the given information. 

x = 75, n = 150 

The lower bound is _______ 

The upper bound is _______ 

Answer 1

Solution :

Given that,

n =150

x = 75

Point estimate = sample proportion = = x / n = 75/150=0.5

1 - = 1- 0.5 = 0.5

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

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

= 1.96 (((0.5*0.5) /150 )

= 0.080

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.5 -0.080 < p < 0.5+ 0.080

0.420< p < 0.580

lower bound =0.420 upper bound 0.580