Answered: (b) How many respondents total were…

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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The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?"

We're interested in examining whether or not there are differences in the typical work week length based on the level of education of the worker. We perform a one-way, independent-samples ANOVA test, with the "groups" in the ANOVA being categories of highest educational degree of the worker ("less than high school," "bachelor's degree," etc.) and the variable being the number of hours written down by the worker in answering the survey question.

(a)Suppose that the results of our ANOVA are given in the ANOVA table below. Complete the missing cell of the ANOVA table (rounding your answer to two decimal places).

Source of variation	Degrees of freedom	Sum of squares	Mean square
Treatments (between groups)	3	299	99.67
Error (within groups)	1105	105,000.7	95.02
Total	1108	105,299.7

(b) How many respondents total were examined in the ANOVA?
(c) For the ANOVA test, it is assumed that the population variance of hours worked per week is the same for each population of workers represented. What is an
unbiased estimate of this common population variance based on the sample variances?
(d) Using the 0.05 level of significance, what is the critical value of the F statistic for the ANOVA test? Round your answer to at least two decimal places.
(e) From the survey data, can we conclude that at least one of the populations differs significantly from the others in mean hours worked in a typical week? Use
the 0.05 level of significance.
O Yes
O No

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