Question

SAMPLE SIZE 4: A confidence interval for the average time it takes a prospective employee to take a basic skills test is to be constructed at a 99.74% confidence. If the population deviation for the data in question is 18 minutes, and the researcher desires a margin of error of 1.4 minutes, then what should be the sample size?

Please write out the formula clear, the answer to this problem is 1488 +/- 1

Answer 1

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The formula is:

The 99.74% Confidence means that we want a standard deviation which corresponds to a Z score of +/- 3

So, Z = +/- 3 ( from empirical rule of normal distribution)

Now, Population deviation = 18 min

Margin of error = Z*Stdev/sqrt(n), where n = sample size

1.4 = 3*18/sqrt(n)

n = (3*18/1.4)^2 = 1487.755 or 1488 +/- 1 ( as sample size can't be in fractions)

Answer: 1488 +/- 1