Question

If n = 540 and ˆpp^ (p-hat) = 0.7, construct a 90% confidence interval.

Give your answers to three decimals

_______ < p < ____

Answer 1

Given that,

Point estimate = sample proportion = =0.7

1 -   = 1-0.7 =0.3

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z  0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.7*0.3) /540 )

E = 0.032

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.7 - 0.032 < p < 0.7+0.032

_0.668 < p < _0.732___