Question

In a survey of 262 smokers , 189 smokers considered themselves addicted to cigarettes.

A.) Find a point estimate for p, smokers that considered themselves addicted.

B.) Construct a 95% C.I. for the population proportion.

C.) Construct a 99% C.I. for the population proportion.

Answer 1

Solution :

Given that,

A) Point estimate = sample proportion = = x / n = 189 / 262 = 0.721

1 - = 1 - 0.721 = 0.279

B) Z/2 = Z0.025 = 1.96  

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

= 1.96 (((0.721 * 0.279) / 262)

= 0.054

A 95% confidence interval for population proportion p is ,

± E

= 0.721   ± 0.054

= ( 0.667, 0.775 )

C) Z/2 = Z0.005 = 2.576

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

= 2.576 (((0.721 * 0.279) / 262)

= 0.071

A 99% confidence interval for population proportion p is ,

± E

= 0.721   ± 0.071

= ( 0.650, 0.792 )