Question

If

n equals=100

and

X equals=20

construct a

90​%

confidence interval estimate for the population proportion

Answer 1

solution

n = 100

x = 20

Point estimate = sample proportion = = x / n =20/100=0.2

1 -   = 1-0.2 =0.8

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.2*0.8) / 100)

= 0.067

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.2 - 0.067 < p < 0.2+0.067

0.133< p < 0.267