Concept explainers
Choosing a Test
a. You wish to test whether an association exists between a categorical variable (such as rank of a professor at a university. assuming four ranks) and a numerical variable (such as yearly salary).
b. You wish to test whether the means of a numerical variable are different for two possible values of a categorical variable (such as yearly salary for gender).
Determine the appropriate test to test whether there is an association between categorical and numerical variables.
Answer to Problem 1SE
ANOVA test is used to test the association between categorical and numerical variables.
Explanation of Solution
Reasons for correct answer:
ANOVA s a parametric statistical test which is used to test the differences among the group means in a sample or population. In ANOVA test, we assume that the sample is drawn from normally distributed population and the population variance is equal.
In this case, one variable is numerical (yearly salary) and other variable is categorical (4 ranks of a professor). So, there are four groups and ANOVA is the only parametric test which is used to compares the means of more than two populations.
Reasons for incorrect answers:
One-sample t-test is used to test whether the sample mean is significantly different from known or hypothesized value. So, we cannot use this test to compare the mean of more than two populations.
Two-sample t-test is used to test whether the two population mean is equal or not. So, this test is not suitable to compare the means of more than two populations.
Chi square test is a non-parametric statistical test is used to determine the relationship between two categorical variables. Chi-square is not a appropriate test for numerical variable. So, we cannot use a chi square test because one variable (yearly salary) is numerical.
Want to see more full solutions like this?
Chapter 11 Solutions
Introductory Statistics (2nd Edition)
Additional Math Textbook Solutions
Statistics Through Applications
Introduction to Statistical Quality Control
Statistics for Psychology
APPLIED STAT.IN BUS.+ECONOMICS
Statistics for Business and Economics (13th Edition)
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL