Question

In a survey of 1,000 people, 420 are opposed to the tax increase. Construct a 95 percent confidence interval for the proportion of those people opposed to the tax increase.

Answer 1

Solution :

n = 1,000

x = 225

= x / n = 420 / 1,000 = 0.420

1 - = 1 - 0.420 = 0.580

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 = 1.960

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

= 1.960 * (((0.420 * 0.580) /1,000)

= 0.030

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.420 - 0.030< p < 0.420 + 0.030

0.390 < p < 0.450