Question

We want to estimate the proportion of unemployed people in Quebec. Taking a sample of 350 adults randomly selected from the workforce, we find that 42 people are out of work. Build a 99% confidence interval for the true proportion of unemployed in Quebec.

Answer 1

Solution :

Given that,

n = 350

x = 42

Point estimate = sample proportion = = x / n = 42/350=0.12

1 -   = 0.88

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576* (((0.12*0.88) /350 )

E = 0.045

A 99% confidence interval for proportion p is ,

- E < p < + E

0.12-0.045 < p < 0.12+0.045

0.075< p <0.165