Question

from a population with a standard deviation of 35, a sample of 150 items is selected. at 95% confidence, what is the margin of error for the population mean? round your answer to three decimal places.

Answer 1

The margin of error for the population mean is 5.601

What does the term "margin of error" mean?

Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.

Given c = 0.95

The significance level is obtained as follows:

alpha = 1 - c

alpha = 1 - 0.95

alpha = 0.05

Also, it is given that n = 150 and sigma = 35 .

The critical value of Z distribution at 0.05 level of significance can be computed in MS Excel using + NORMS INV (alpha/2) function as follows:

Thus, $Z_{0.005/2}=1.96$

Now, the margin of error can be computed as follows: ME = Critical Value x Standard Error

$Z_{0.005/2}*\frac{sigma}{\sqrt{n} } \\= 1.96 * \frac{35}{\sqrt{150} } \\= 5.601$

Thus, the margin of error for the population mean is 5.601

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