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

See similar textbooks

Related questions

Question

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

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 + ...

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Anova and Design of Experiments$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions