Does college grade point average (GPA) depend on gender? Does it depend on class (freshman, sophomore, junior, senior)? In a study, the following GPA data were obtained for random samples of college students in each of the cells. Class Gender Freshman Sophomore Junior Senior Male 2.8 2.12.7 3.0 2.5 2.32.9 3.5 3.1 2.93.2 3.8 3.8 3.63.5 3.1 Female 2.3 2.93.5 3.9 2.6 2.43.3 3.6 2.6 3.63.3 3.7 3.2 3.53.8 3.6 Minitab Printout of GPA Based on Gender and Class Analysis of Variance for GPA Source DF SS MS F P Gender 1 0.281 0.281 1.26 0.273 Class 3 2.226 0.742 3.32 0.037 Interaction 3 0.286 0.095 0.43 0.736 Error 24 5.365 0.224 Total 31 8.159 (b) Use two-way ANOVA and the Minitab printout to determine if there is any evidence of interaction between the two factors at a level of significance of 0.05. F = P-value = (c) If there is no evidence of interaction, use two-way ANOVA and the Minitab printout to determine if there is a difference in mean GPA based on class. Use α = 0.05. (Enter NONE in any unused answer blanks.) F = P-value = d) If there is no evidence of interaction, use two-way ANOVA and the Minitab printout to determine if there is a difference in mean GPA based on gender. Use α = 0.05. (Enter NONE in any unused answer blanks.) F = P-value =

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Does college grade point average (GPA) depend on gender? Does it depend on class (freshman, sophomore, junior, senior)? In a study, the following GPA data were obtained for random samples of college students in each of the cells.

	Class
Gender	Freshman	Sophomore	Junior	Senior
Male	2.8 2.1 2.7 3.0	2.5 2.3 2.9 3.5	3.1 2.9 3.2 3.8	3.8 3.6 3.5 3.1
Female	2.3 2.9 3.5 3.9	2.6 2.4 3.3 3.6	2.6 3.6 3.3 3.7	3.2 3.5 3.8 3.6

Minitab Printout of GPA Based on Gender and Class
Analysis of Variance for GPA
Source	DF	SS	MS	F	P
Gender	1	0.281	0.281	1.26	0.273
Class	3	2.226	0.742	3.32	0.037
Interaction	3	0.286	0.095	0.43	0.736
Error	24	5.365	0.224
Total	31	8.159

(b) Use two-way ANOVA and the Minitab printout to determine if there is any evidence of interaction between the two factors at a level of significance of 0.05.

F	=
P-value	=

(c) If there is no evidence of interaction, use two-way ANOVA and the Minitab printout to determine if there is a difference in mean GPA based on class. Use α = 0.05. (Enter NONE in any unused answer blanks.)

F	=
P-value	=

d) If there is no evidence of interaction, use two-way ANOVA and the Minitab printout to determine if there is a difference in mean GPA based on gender. Use α = 0.05. (Enter NONE in any unused answer blanks.)

F	=
P-value	=

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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