A college dean wants to determine the average time it takes a student to get from one class to the next.Preliminary studies have shown that it is reasonable to let _t = 1.5 minutes the standard deviation of class travel times).What is the sample size which should be examined if the dean wants to assert with a probability of 95 percent that his estimate, the mean time of the random sample, will not be "off" by more than .25 minutes in either direction)? Choose the closest answer. A)72 or more, but not less B)81 or more, but not less C)139 or more, but not less D)200 or more, but not less E)None of the above

Question

Quizplus · Accepted Answer

We can use the formula for sample size calculation for mean:
n = ((Z-score * standard deviation) / margin of error )^2

Where Z-score for 95% confidence interval is 1.96
standard deviation (s) = 1.5
margin of error (E) = 0.25

Substituting the values,
n = ((1.96 * 1.5) / 0.25)^2 = 138.2976

Rounding up to the nearest integer, we get n = 139. Therefore, the sample size which should be examined is 139 or more, but not less. Option C is the closest.

A College Dean Wants to Determine the Average Time It