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

Answer:

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

Step-by-step 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±$\frac{z*\sqrt{p*(1-p)}}{\sqrt{N} }$ 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±$\frac{1.96*\sqrt{0.70*0.30}}{\sqrt{250} }$≈ 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.