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Answer:
The 95% confidence interval would be given (0.419;0.481).
Step-by-step explanation:
Data given and notation
n=1000 represent the random sample taken
X=450 represent the people in the sample favored Candidate A
estimated proportion of people in the sample favored Candidate A
represent the significance level
Confidence =0.95 or 95%
p= population proportion of people in the sample favored Candidate A
Solution to the problem
The confidence interval would be given by this formula
For the 95% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 95% confidence interval would be given (0.419;0.481).
We are confident (95%) that about 41.9% to 48.1% of the people are favored Candidate A.