A random survey of 2000 people is made & 900 responded affirmatively (so p = 0.45)....

A random survey of 2000 people is made & 900 responded affirmatively (so p = 0.45). Build & interpret a 95% confidence interval.

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Expert Solution

Solution :

Given that,

n = 2000

x = 900

Point estimate = sample proportion = = x / n = 900/2000=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 * $\sqrt$ ((( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((0.45*0.55) /2000 )

E = 0.022

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.45-0.022 < p < 0.45+0.022

0.428< p < 0.472

orchestra answered 1 year ago

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