Random samples of two freshmen, two sophomores, two juniors, and two seniors each from four dormitories were asked to rate, on a scale of 1 (poor) to 10 (excellent), the quality of the dormitory environment for studying. The results are shown in the attached table:
a. Set up the analysis of variance table. b. Test the null hypothesis that the population mean ratings are the same for the four dormitories. c. Test the null hypothesis that the population mean ratings are the same for the four student years. d. Test the null hypothesis of no interaction between student year and dormitory rating.
Transcribed Image Text:Dormitory
Year
A
B
C
D
Freshman
7
8
6
9
Sophomore
8.
8.
Junior
4
6.
7
7
Senior
4
6
8
5
6.
7
976N
657
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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