Question

Write a confidence interval problem using one of the options below.

Think about a population proportion that you may be interested in and propose a confidence interval problem for this parameter.Your data values should be approximately normal.

"In a survey conducted among 100 men reports that 16 out of those 100 males are heavy smokers. With a 95% Confidence Interval for the population proportion of the 16 males that reported being heavy smokers."

Answer 1

Solution :

Given that,

n = 100

x = 16

Point estimate = sample proportion = = x / n = 16 / 100 = 0.16

1 - = 1 - 0.16 = 0.84

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z _0.025 = 1.96

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

= 1.96 * (((0.16*0.84) /100 )

= 0.072

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.16 - 0.072 < p < 0.16 + 0.072

0.088 < p < 0.232

The 95% confidence interval for the population proportion p is : (0.088 , 0.232)