A manager wishes to determine whether the mean times required to complete a certain project differ for the three levels of employee training. He randomly selected 8 employees with each of the three levels of training (beginner, intermediate, and advanced). Does the data provide sufficient evidence to indicate that the mean times required to complete a certain task differ based on training? Beginner: 10.5,11.0,15.5,21.5,32.0,12.0,22.5,20.0 Intermediate: 6.5,10.5,11.0,7.5,18.0,7.0,14.5,13.5 Advanced: 3.5,7.5,10.25,6.25,4.0,5.75,2.5,3.5 Beginner Mean: 19.38 Intermediate Mean: 11.06 Advanced mean: 5.41 Grand Mean: 11.95 Dependent variable: time in hours to complete the project (continuous DV) Independent variable: level of training (categorical: beginner, intermediate, advanced) Please show work and write using proper statistical notation What are the null and alternative hypotheses for this one-way ANOVA? Using a one-way ANOVA, is there a significant difference among the levels of training at p < .05 Using a topic of your own interest, develop a study that can be analyzed using a one-way ANOVA. The example must include one categorical IV, and one continuous DV, and be a between subjects design. You don’t need to conduct the ANOVA, just discuss the types of variables and the types of data required.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A manager wishes to determine whether the mean times required to complete a certain project differ for the three levels of employee training. He randomly selected 8 employees with each of the three levels of training (beginner, intermediate, and advanced). Does the data provide sufficient evidence to indicate that the mean times required to complete a certain task differ based on training?

Beginner: 10.5,11.0,15.5,21.5,32.0,12.0,22.5,20.0

Intermediate: 6.5,10.5,11.0,7.5,18.0,7.0,14.5,13.5

Advanced: 3.5,7.5,10.25,6.25,4.0,5.75,2.5,3.5

Beginner Mean: 19.38

Intermediate Mean: 11.06

Advanced mean: 5.41

Grand Mean: 11.95

Dependent variable: time in hours to complete the project (continuous DV)

Independent variable: level of training (categorical: beginner, intermediate, advanced)

Please show work and write using proper statistical notation

What are the null and alternative hypotheses for this one-way ANOVA?
Using a one-way ANOVA, is there a significant difference among the levels of training at p < .05

Using a topic of your own interest, develop a study that can be analyzed using a one-way ANOVA. The example must include one categorical IV, and one continuous DV, and be a between subjects design. You don’t need to conduct the ANOVA, just discuss the types of variables and the types of data required.

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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