Question

The Philadelphia Area Transit Authority wishes to estimate the proportion of central city workers that use public transportation to get to work. A sample of 100 workers revealed that 64 used public transportation. Develop a 95% confidence interval for the population proportion.

Answer 1

Out of 100 workers 64 used public transportation so the sample proportion is,

p̂ = 64/100 = 064

 

The sample size is,

n = 100

 

From z table, for 95% confidence interval, the critical value of z is zα/2 = 1.96.

 

The 95% confidence interval for population proportion will be,

p̂ ± 1.96√p̂(1 – p̂)/n = 0.64 ± 1.96√0.64(1 – 0.64)/100

                                 = 0.64 ± 0.0941

                                 = (0.5459, 0.7341)

 

Hence, 95% confidence interval for population proportion will be (0.5459, 0.7341).

Hence, 95% confidence interval for population proportion will be (0.5459, 0.7341).