Question

If n=490 and ˆ p (p-hat) = 0.31, construct a 90% confidence interval. Give your answers to three decimals.

Answer 1

Solution :

Given that,

n = 490

Point estimate = sample proportion = =0.31

1 -   = 1-0.31 =0.69

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.31*0.69) / 490)

= 0.0344

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.31 -0.0344 < p < 0.31 + 0.0344

0.2756< p < 0.3444

The 90% confidence interval for the population proportion p is : 0.2756, 0.3444