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Practice question 3. If the actual support for presidential candidate A was 50%, what is the...

Practice question 3.

  1. If the actual support for presidential candidate A was 50%, what is the probability that the estimate obtained from a sample of 1,600 people would be less than 48%?
  2. In the Presidential Poll, 1,600 people were interviewed, and 720 of those interviewed said they supported candidate A. Determine the point estimate for A’s support.
  3. What is the mean error of this estimate?
  4. Specify a 99% confidence interval for the (actual) percentage of support.
  5. Specify a 99.9% confidence interval for the (actual) percentage of support.
  6. If 50% of the votes are needed to win, how credible do you find A’s win?

Solutions

Expert Solution

P(z<Z) table :

a.

mean = actual support = 50% = 0.50

mean error = SE = [0.50*(1-0.50)/1600]

= 0.00015625

SD = n*SE = 1600*0.00015625 = 0.25

P(sample proportion <= 48% ) :

b.

point estimate of support = proportion of support

= 720/1600

= 0.45

= 45%

c.

p = point estimate

mean error = [ p*(1-p) / n ]

= [0.45*0.55/1600]

= 0.00015

= 0.015 %

d.

actual percentage (support) = 50%

99% confidence interval for percentage of support : [46.8%, 53.2%]

(please upvote)

orchestra answered 1 year ago
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