Margin of Error and Confidence Interval for a Poll
A recent poll (fictitious) reports that President Obama's "approval rating" is 52% and a statement says, "This poll has an error rate of 3%." The poll sampled 1300 people. (Note: The "3%" is the "margin of error." There is no computation of the confidence interval formula needed).
This is an application of a confidence interval on a proportion.
Compute the confidence interval on the proportion using the data given. How does the "3%" come about?
Interpret the confidence interval. Do the majority of the people in the country, based on the sample (and assume it is a good sample) approve of the President's actions? If so, why? f no, why?
What if the percent approval was 58% with the same margin of error?
What if the percent approval was 46% with the same margin of error?
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Solution Preview
Compute the confidence interval on the proportion using the data given. How does the "3%" come about?
The confidence interval will be
= (0.52 - 0.03, 0.52 + 0.03)
= (0.49, 0.55)
I am assuming that z is taken to be 1.96.
That is we are calculating a 95% confidence interval.
Margin of error = z*sqrt(pq/n) = 1.96*sqrt(0.52*(1-0.52)/1300) = 0.03 ...
Solution Summary
Using the data from the poll, the confidence interva is found and analysed for the primary and two alternate situations.