According the course handbook at a large university, the length of classes held on Monday (M), Wednesday (W), and Friday (F) have a mean of 50 minutes and standard deviation of 5 minutes. The length of classes held on Tuesdays (T) and Thursdays (R) have a mean of 75 minutes and standard deviation of 7 minutes. The college provost is concerned that professors that teach classes on Tuesdays and Thursdays are dismissing their students too early. To determine if there is credibility about this concern the provost selects a random sample of 30 TR classes and 30 MWF classes and determines the length of each class. Let xTR - xMWF be the difference in the sample mean class length for the two types of classes.

(a) What is the shape of the sampling distribution of xTR – xMWF? Why?
(b) Find the mean of the sampling distribution.
(c) Verify that the 10% condition is met, then calculate the standard deviation of the sampling distribution.
(d) What is the probability that the difference in sample means is less than 20 minutes?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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