if a polling result states that a president has an approval rating of 55%, with a margin of error of x, how should you interpret that?

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01-12-2022
Mathematics

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if a polling result states that a president has an approval rating of 55%, with a margin of error of x, how should you interpret that?

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smecloudbird18 smecloudbird18 · Answer 1 · 2022-12-06T01:36:28-05:00

At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, the value of a margin of error of x is 1.534%.

In the given question, at a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, then we have to explain how should we interpret that.

The given confidence interval = 95%.

We can write it as CI = 0.95.

An approval rating is 55%.

We can write it as(p) = 0.55

A margin of error is x.

Let the value of sample size n = 1000.

So the margin of error;

ME = z× {p(1-p)}/√n

The value of z for confidence interval of 95% is 1.96.

Now putting the value

x = 1.96× {0.55(1-0.55)}/√1000

x = 1.96× {0.55×0.45}/31.623

x = 1.96× 0.2475/31.623

x = 1.96×0.00783

x = 0.01534

x = 1.534%

So the margin of error should be 1.534%.

To learn more about confidence interval link is here

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The right question is:

At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, how should you interpret that?