Question

A sample of 1100 observations taken from a population produced a sample proportion of 0.36. Make a 90% confidence interval for p.

Round your answers to three decimal places.

Answer 1

Solution :

Given that,

= 0.39 n=1100

1 - = 1 - 0.36 = 0.64

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.36 * 0.64) / 1100) = 0.024

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.36 - 0.024 < p < 0.36 + 0.024

0.336 < p < 0.384