Question

You read about a survey in a newspaper and find that 70% of the 250 people sampled prefer Candidate A. You are surprised by this survey because you thought that more like 50% of the population preferred this candidate. Based on this sample, is 50% a possible population proportion?

Answer 1

50% is not a possible population proportion who support candidate A.

Explanation:

I will estimate 95% confidence interval to see if 50% a possible population proportion who support candidate A.

95% Confidence Interval can be calculated using

CI=p±
`(z*√(p*(1-p)))/(√(N) )` where

• z is the corresponding statistic in 95% confidence level (1.96)

• p is the sample proportion who support candidate A (70% or 0.70)

• N is the sample size (250)

Then CI=0.70±
`(1.96*√(0.70*0.30))/(√(250) )`≈ 0.70±0.06

That is 95% confidence interval is (64%, 76%). Since 50% is less than lower CI limit, 50% is not a possible population proportion who support candidate A.