From a random sample of potential voters in an upcoming election 47% indicated they intended to vote for candidate R A 95 percent confidence interval was constructed from the sample and the margin error for the estimate was 5%

The 95% confidence intervals of given margin error

(0.42 , 0.52)

Explanation:

Step 1:-

The 95% confidence intervals of given margin error

x⁻ ± M.E

The 95% confidence intervals of given margin error

  (        , )

Now given  random sample of potential voters in an upcoming election 47%

That is The sample of the mean  ( x⁻ ) = 0.47

the margin error for the estimate was  5%

That is  margin error of the sample M.E = = 5% =0.05

Step 2:-

The 95% confidence intervals of given margin error

  (        , )

(0.42 , 0.52)

The interval of the 95% confidence interval is (42%,53%)

The given parameters are:

The 95% confidence intervals of margin of error is calculated using:

So, we have:

Expand the above equation

Hence, the interval of the 95% confidence interval is (42%,53%)

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