Construct a ​95% confidence interval of the population proportion using the given information. x=80 n =200

1 answer
Question:

Construct a ​95% confidence interval of the population proportion using the given information. x=80 n =200

Answers

95% confidence interval of the population proportion is  (0.227, 0.373)

Step-by-step explanation:

Confidence Interval can be calculated using p±ME where

p is the population proportion ([tex]\frac{45}{150} =0.3[/tex]ME is the margin of error from the mean

and margin of error (ME) around the mean can be found using the formula

ME=[tex]\frac{z*\sqrt{p*(1-p)}}{\sqrt{N} }[/tex] where

z is the corresponding statistic in 95% confidence level (1.96)p is the population proportion (0.3)N is the sample size (150)

then ME=[tex]\frac{1.96*\sqrt{0.3*0.7}}{\sqrt{150} }[/tex] ≈ 0.073

Then 95% confidence interval would be 0.3±0.073 or (0.227, 0.373)

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