Question

Of a random sample of 600 trucks at a bridge, 132 had bad signal lights. Construct a 95 percent confidence interval for the percentage of trucks that had bad signal lights.

Answer 1

Solution :

Given that,

n = 600

x = 132

= x / n = 132 / 600 = 0.220

1 - = 1 - 0.220 = 0.780

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 * (((0.220 * 0.780) / 600)

= 0.033

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.220 - 0.033 < p < 0.220 + 0.033

0.187 < p < 0.253

The 95% confidence interval for the population proportion p is : ( 18.7% , 25.3%)