Question

Construct a 95​% confidence interval to estimate the population proportion with a sample proportion equal to

0.45 and a sample size equal to 120.

----- A 95% confidence interval estimates that the population proportion is between a lower limit of

___ and an upper limit of ___

????

Answer 1

Solution :

Given that,

n = 120

Point estimate = sample proportion = =0.45

1 -   = 1- 0.45 =0.55

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.45*0.55) /120 )

= 0.089

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.45-0.089 < p < 0.45+0.089

0.361< p < 0.539

A 95% confidence interval estimates that the population proportion is between a lower limit of

0.361___ and an upper limit of _0.539__