How likely are you to vote in the next presedential election? A random sample of

Question

How likely are you to vote in the next presedential election? A random sample of 300 adults was taken, and 192 of them said that they always vote in prersedential elections.

a) Construct a 95% confidence interval for the proportion of adult Americans who say they always vote in presedential elctions

b) An article in American Demographic reports this percentage of 67%. Based on the interval constructed in part a, would you disagree with their reported percentage? Explain.

c) Can we use the interval estimate from part a to estimate the actual proportion of adult Americans who vote in the 2004 presedential election? Why or why not?

Explanation / Answer

Solution(a)

sample proportion =p^=x/N=192/300=0.64

sample size=n=300

95% confidence interval for the population proportion is given by:

Z multiplier for 95% confidence level=1.96

Reference table:

substituting this values we get 95% CI for population proportion:

0.64±1.96 sqrt{0.64(1-.64)/300}

=0.64±0.054

=0.64-0.054<p<0.64+0.054

=0.586<p<0.694

lower boundary=0.586

upper boundary=0.694

we are 95% confident that the true population proportion lies in between 0.586=58.6% and 0.694=69.4%

Solution(b):

I would agree with reported percentage as 67% lies in between the confidence interval for population proprtion.

58.6%<67%<69.4%

67% more than lower boundary 58.6%

and less than upper boundar 69.4%

Solution(C):

Yes

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