Question

The 95% confidence interval for a population mean (context unknown and irrelevant) turns out to be (428, 510). What is E?

Answer 1

The 95% confidence interval for a population mean has a margin of error (E) of 41

The confidence interval for a population mean is given by:

Confidence interval = μ ± E = (μ - E, μ + E)

Where μ is the mean and E is the margin of error.

Since the confidence interval is (428, 510), hence:

μ - E = 428      (1)

μ + E =  510     (2)

Subtracting equation 1 from equation 2:

2E = 82

E = 41

μ - E = 428

μ -41 = 428

μ = 469

Hence the margin of error (E) is 41

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