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YOU MEET 80 RANDOMLY SELECTED VOTERS AND FIND THAT 54% SUPPORT A CANDIDATE FOR THE LEGISLATURE OF MONAGAS. USING A CONFIDENCE LEVEL OF 95% CALCULATE THE LIMIT OF PERCENTAGE OF VOTERS WHO PREFER THE REFERRED CANDIDATE?
shirley mogollon
The confidence interval for this problem can be calculated using the following formula:
Confidence Interval = p ± z*√(p*(1-p)/n)
Where:
p = observed proportion (54%)
n = sample size (80)
z = z-score (1.96)
Confidence Interval = 0.54 ± 1.96*√(0.54*(1-0.54)/80)
Confidence Interval = 0.54 ± 0.07
Therefore, the confidence interval is 0.47 - 0.61, meaning that we can be 95% confident that the percentage of voters who prefer the referred candidate is between 47% and 61%.
David Denton
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