Question

Construct the 95% confidence interval for the proportions of US adults who think that teenagers are the most dangerous drivers.

A Gallup poll surveyed 900 randomly sampled Americans and found that 63% of them said they would rate teenagers as the most dangerous drivers.

Show all the steps. Use correct symbols and formulas. Interpret the results

Answer 1

Solution :

n = 900

= 0.63

1 - = 1 - 0.630 = 0.370

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.960 * (((0.630 * 0.370) / 900)

= 0.031

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.630 - 0.031 < p < 0.630 + 0.031

0.598 < p < 0.661