Question

If n = 240 and ˆ p (p-hat) = 0.7, construct a 99% confidence interval. Give your answers to three decimals

< p <

Answer 1

Solution :

Given that,

n = 240

Point estimate = sample proportion = = 0.7

1 - = 1 - 0.7 = 0.3

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 (((0.7*0.3) /240 )

= 0.076

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.7 - 0.076 < p < 0.7 + 0.076

0.624< p < 0.776

The 99% confidence interval for the population proportion p is : (0.624 , 0.776)