Question

If n=200 and X=70​, construct a 90​% confidence interval estimate for the population proportion.

Answer 1

Solution :

Given that,

n = 200

x = 70

Point estimate = sample proportion = = x / n = 70/200=0.35

1 - = 1-0.35=0.65

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table )

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

= 1.645 (((0.65*0.35) /200 )

E = 0.0555

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.65 -0.0555< p < 0.65+0.0555

0.5945< p < 0.7055

The 90% confidence interval for the population proportion p is : 0.5945, 0.7055