Q9: How likely are you to vote in the next presidental election? A random sample
ID: 3159490 • Letter: Q
Question
Q9: How likely are you to vote in the next presidental election? A random sample of 300 adults was taken, an d192 of them said that they always vote in presidental elections.
(a) Construct a 95% confidence interval for the proportion of adult Americans who say they always vote in presidental elections.
(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 acutal proportion of adult Americans who vote in the 2004 presidental election? Why or why not?
Explanation / Answer
a)
Note that
p^ = point estimate of the population proportion = x / n = 0.64
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.027712813
Now, for the critical z,
alpha/2 = 0.025
Thus, z(alpha/2) = 1.959963985
Thus,
Margin of error = z(alpha/2)*sp = 0.054316115
lower bound = p^ - z(alpha/2) * sp = 0.585683885
upper bound = p^ + z(alpha/2) * sp = 0.694316115
Thus, the confidence interval is
( 0.585683885 , 0.694316115 ) [ANSWER]
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b)
No, I would not disagree, as 0.67 is inside the interval. [ANSWER]
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c)
No, because maybe some voters in 2004 don't always vote like those who said yes in this survey.
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