5.48 Work hours and education: The General Social Survey collects data on demographics, education, and work, among many other characteristics of US residents. Using ANOVA, we can consider educational attainment levels for all 1,172 respondents at once. Below are the distributions of hours worked by educational attainment and relevant summary statistics that will be helpful in carrying out this analysis. Educational attainment Less than HS (1) HS (2) Jr Coll (3) Bachelor's (4) Graduate (5) Total Mean 38.67 39.6 41.39 42.55 40.85 40.45 SD 15.81 14.97 18.1 13.62 15.51 15.17 n 121 546 97 253 155 1172 (a) Write hypotheses for evaluating whether the average number of hours worked varies across the five groups. ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5 Ha: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5 Ha: At least one pair of means is the same ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5 Ha: At least one of the means is different ( )Ho: μ1 = μ2 = μ3 = μ4 = μ5 = μ6 Ha: At least one of the means is different (b) Below is part of the output associated with this test. Fill in the empty cells (please be accurate to two decimal places). Df Sum Sq Mean Sq F value Pr(>F) degree _____ _ 501.54 _ 0.0682 residuals _ 267382 _ __ _ Total _ _ (c) What is the value of the test statistic associated with this ANOVA test? _____________

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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5.48 Work hours and education: The General Social Survey collects data on demographics, education, and work, among many other characteristics of US residents. Using ANOVA, we can consider educational attainment levels for all 1,172 respondents at once. Below are the distributions of hours worked by educational attainment and relevant summary statistics that will be helpful in carrying out this analysis.

Educational attainment

	Less than HS (1)	HS (2)	Jr Coll (3)	Bachelor's (4)	Graduate (5)	Total
Mean	38.67	39.6	41.39	42.55	40.85	40.45
SD	15.81	14.97	18.1	13.62	15.51	15.17
n	121	546	97	253	155	1172

(a) Write hypotheses for evaluating whether the average number of hours worked varies across the five groups.

( )Ho: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
Ha: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅
( )Ho: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
Ha: At least one pair of means is the same
( )Ho: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
Ha: At least one of the means is different
( )Ho: μ₁ = μ₂ = μ₃ = μ₄ = μ₅ = μ₆
Ha: At least one of the means is different

(b) Below is part of the output associated with this test. Fill in the empty cells (please be accurate to two decimal places).

	Df	Sum Sq	Mean Sq	F value	Pr(>F)
degree	_________	_________	501.54	_________	0.0682
residuals	_________	267382	_______	________	_________
Total	________	________	________	_________	_________

(c) What is the value of the test statistic associated with this ANOVA test? _________________
(please round to two decimal places)

80
60
40
20
Less than HS
HS
Jr Coll
Bachelor's
Graduate
00
HI
Hours worked per week

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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