A career counselor wants to understand if the average annual earnings differ by educational attainment. The counselor uses three education levels: high school or less, undergraduate degree, and master's degree or more. After collecting data, the resulting incomplete one-way ANOVA table and Tukey's confidence intervals are shown below. Source of VariationSSdfMSFBetween Degrees 1,936 Within Degrees Total8,05424 LowerUpperUndergraduate–High School8.2343.11Master's–High School11.8946.77Master's–Undergraduate-12.6519.98 Complete the ANOVA table. Set up the competing hypothesis to test whether there are differences in mean annual salary between the different education levels. At the 5% significance level, what is the conclusion to the test? If significant differences exist, use Tukey's confidence intervals to determine which educational levels have different mean annual earnings.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A career counselor wants to understand if the average annual earnings differ by educational attainment. The counselor uses three education levels: high school or less, undergraduate degree, and master's degree or more. After collecting data, the resulting incomplete one-way ANOVA table and Tukey's confidence intervals are shown below.

*Source of Variation*	SS	df	MS	F
Between Degrees			1,936
Within Degrees
Total	8,054	24

	Lower	Upper
Undergraduate–High School	8.23	43.11
Master's–High School	11.89	46.77
Master's–Undergraduate	-12.65	19.98

Complete the ANOVA table.

Set up the competing hypothesis to test whether there are differences in mean annual salary between the different education levels.

At the 5% significance level, what is the conclusion to the test?

If significant differences exist, use Tukey's confidence intervals to determine which educational levels have different mean annual earnings.

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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