Question

of 200 adults randomly selected from one town 43 of them smoke. find the best point estimate for the proportion of all adults in town who smoke. for a 95% confidence interval for the true proportion of all adults in the town who smoke, what is the margin of error ? round up to three decimal places.

Answer 1

Solution :

Given that,

n = 200

x = 43

Point estimate = sample proportion = = x / n = 43/200=0.215

1 -   = 1-0.215 =0.785

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.215*0.785) / 200)

E = 0.0569

Margin of error = E = 0.057