Question

Hardly a day goes by without some new poll being published. Polls influence the choice of candidates and the direction of their policies, especially during election campaigns. For example, the Gallup Organization polled 1012 American adults, asking them, ``Do you think there should or should not be a law that would ban the possession of handguns, except by the police and other authorized persons?'' Of 1012 randomly chosen respondents, 374 said that there should be such a law. Construct a 95% confidence interval for the population proportion of all American adults who think there should be such a law.

Answer 1

Solution :

Given that,

n = 1012

x = 374

Point estimate = sample proportion = = x / n = 374 / 1012 = 0.370

1 - = 1 - 0.37 = 0.630

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 * (((0.370 * 0.630) / 1012)

= 0.030

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.370 - 0.030 < p < 0.370 + 0.030

0.340 < p < 0.400

The 95% confidence interval for the population proportion p is : (0.340 , 0.400)