A national survey conducted in 2015 among a simple random sample of 1,507 adults

Question

A national survey conducted in 2015 among a simple random sample of 1,507 adults shows that 56% of Americans think the Civil War is still relevant to American politics and political life. a) Calculate a 90% confidence interval for the proportion of Americans who think the Civil War is still relevant b) Interpret the interval in the context of the question. c) If someone claims that in fact less than 50% of all Americans think the Civil War is still relevant to American politics and political life, does your confidence interval support his/her claim?

Explanation / Answer

a) here p=0.56 ; n=1507

hence std error =(p(1-p)/n)1/2 =0.0128

for 90% CI; z=1.6449

hence confidence interval =mean -/+ z*std error =0.539 ; 0.581

b) this confidence interval gives 95% probability to contain true proportion of average american who think civil war is still relevent

c)as our confidence interval does not contain 50% as probable values our confidence intervaldoes not support his/her claim

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