Question

The Business Education Department has six full-time faculty members. At their monthly department meeting, each full-time faculty member reported the number of hours they taught during the past month:

Faculty Member Teaching Hours

Bernhardt 84, Haas 92, England 84, Pecord 83, Hines 92, Tanner 83

A. Calculate the population mean for the six full-time faculty members:

B. If two full-time faculty members are selected randomly, how many different samples are possible?

C. Calculate the sample means:

D. Calculate the sampling distribution:

Answer 1

(A)

Population Mean () is given by:

So,

Answer is:

86.3333

(B)

Number of different samples = 6C2 = 15

So,

Answer is:

15

(C)

The sample means are got as follows:

Sample	Mean
84,92	88
84,84	84
84,83	83.5
84,92	88
84,83	83.5
92,84	88
92,83	87.5
92,92	92
92,83	87.5
84,83	83.5
84,92	88
84,83	83.5
83,92	87.5
83,83	83
92,83	87.5

(D)

The Sampling Distribution is got as follows:

n = 15

Mean of Sampling Distribution of Sample means is given by

x	x-	(x-)2
88	1.6667	2.7778
84	-2.3333	5.4444
83.5	-2.8333	8.0278
88	1.6667	2.7778
83.5	-2.8333	8.0278
88	1.6667	2.7778
87.5	1.1667	1.3611
92	5.6667	32.1111
87.5	1.1667	1.3611
83.5	-2.8333	8.0278
88	1.6667	2.7778
83.5	-2.8333	8.0278
87.5	1.1667	1.3611
83	-3.3333	11.1111
87.5	1.16667	1.3611
Total =		97.3333

Standard Deviation of Sampling Distribution of Sample means is given by

So

Answer is:

The Sampling Distribution of Sample means is Normal Distribution with mean = 86.3333 and Standard Deviation = 2.5473