Question

From a phone survey, a researcher determined that the true estimate for the proportion of voters who will reelect the mayor is likely to be in the interval (0.39,0.47) what is the survey's margin of error? _______+ The results of a poll indicate that between 46% and 52% of consumers prefer Drink A to Drink B.. The poll selected 1500 randomly selected consumers. What is the interval for the number of consumers who are likely to prefer Drink A to Drink B, in the form (lower limit, upper limit).

Answer 1

First of all, I must confess that I've never studied or used this stuff, so the following in-depth analysis is brought to you direct from the seat of my pants:

-- If the portion of voters is in the interval (0.39, 0.47),
then it's 0.43 ± 0.04 .
It looks like the survey predicts 43% with a margin of error of ±4% .

-- 1500 consumers were surveyed.
46% of them amounts to 690 people.
52% of them amounts to 780 people.

The interval for the number of consumers
who are likely to prefer Drink-A is (690, 780) .

Note:
I have no confidence in my answers, and you should take the hint.
Past results are not a guarantee of future performance.
Your results depend on how you drive.
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Not a member of FDIC.

Answer 2

a) The error margins for p = 0.39 and p = 0.47 respectively are
`(0.956)/(√(n) )` and
`(0.978)/(√(n) )`

b1) number of consumers that prefer drink A = 690

b2) number of consumers that prefer drink A = 780

Explanation:

Formula for error margin:

`Error margin = z\sqrt{(p(1-p))/(n) }`

Let us assume a 96% confidence level. For 96% confidence level, z = 1.96

When true estimate, p = 0.39, the error margin is:

`Error margin = 1.96\sqrt{(0.39(1-0.39))/(n) }\\Error margin = 1.96\sqrt{(0.2379)/(n) }\\Error margin = 1.96*(0.4878)/(√(n) ) \\Error margin = (0.956)/(√(n) )`

When the true estimate, p = 0.47, the error margin is:

`Error margin = 1.96\sqrt{(0.47(1-0.47))/(n) }\\Error margin = 1.96\sqrt{(0.2491)/(n) }\\Error margin = 1.96*(0.499)/(√(n) ) \\Error margin = (0.978)/(√(n) )`

The error margins for p = 0.39 and p = 0.47 respectively are
`(0.956)/(√(n) )` and
`(0.978)/(√(n) )`

b) Sample size = 1500

46% consumers prefer drink A

number of consumers that prefer drink A = 46% of 1500

number of consumers that prefer drink A =
`(46)/(100) * 1500`

number of consumers that prefer drink A = 690

52% of consumers prefer drink B

number of consumers that prefer drink A = 52% of 1500

number of consumers that prefer drink A =
`(52)/(100) * 1500`

number of consumers that prefer drink A = 780