Lab Activity 9
One-Way Analysis of Variance (ANOVA)
Data Set: Hot Dog
One-way analysis of variance is a method for comparing several population means, when the data are
from independent samples. It a test that examines the relationship between a quantitative response
variable and a categorical explanatory variable, also called factor that has at least three levels or groups.
1.
Determining if ANOVA is Appropriate
In each part below determine if ANOVA can be used to analyze the scenario. IF ANOVA can be used,
write the null and alternative hypotheses.
Hint: Since ANOVA is used only in scenarios with a quantitative response variable and
categorical explanatory variable (or factor) that has at least three levels, you may find it helpful
to first identify the response and explanatory variables and determine if they are categorical or
quantitative.
a. A psychologist wants to determine if there is a relationship between weather (sunny, partly
cloudy, heavy rain, etc.) and mood (happy, carefree, tired, etc.).
i. Can ANOVA be used? Explain.
Since both the explanatory (weather) and response (mood) variables are categorical, ANOVA
cannot be used here.
IF ANOVA can be used, write the null and alternative hypotheses:
ii. Ho:
iii. Ha:
b. An executive of a national construction company is trying to determine how to be “low bid” on
more estimates in order to get more jobs. She compares the cost of lumber in dollars in different
regions of the United States, specifically, the North, South, East, and West to generate more accurate
estimates.
i. Can ANOVA be used? Explain.
Since the explanatory variable (region) is categorical and the response variable (cost of lumbar)
is quantitative, ANOVA can be used here.
IF ANOVA can be used, write the null and alternative hypotheses:
ii. Ho: The mean costs of lumber in different regions of the United States are identical.
iii. Ha: At least two regions differ significantly in the mean costs of lumber.

c. An HR manager believes that just because employees work long hours does not mean they are
productive, agreeing with this article, “Get a Life,” from September 24, 2013 in The Economist
(http://www.economist.com/blogs/freeexchange/2013/09/working-hours). To test this, the HR manager
wants to see if there is a relationship between salary, measured by yearly earnings in dollars, and
amount of time worked during the year.
i. Can ANOVA be used? Explain.
Since both the explanatory (amount of time worked) and response (salary) variables are
quantitative, ANOVA cannot be used here.
IF ANOVA can be used, write the null and alternative hypotheses:
ii. Ho:
iii. Ha:
d. A nutritionist wants to see if grocery buying habits vary based on level of education. The nutritionist
compares the average amount spent in dollars on organic food for three different levels of education:
high school diploma, college degree, or advanced degree.
i. Can ANOVA be used? Explain.
Since the explanatory variable (level of education) is categorical and the response variable
(amount spent on organic food) is quantitative, ANOVA can be used here.
IF ANOVA can be used, write the null and alternative hypotheses:
ii. Ho: The mean amounts spent on organic food in different levels of education are identical.
iii. Ha: At least two levels of education differ significantly in the mean amounts spent on organic
food.
e. Given the recent news of Ebola, the US government is trying to keep everyone living in the US at
ease. A government official wants to see if their efforts have been successful. He interviews 100
people of various age groups (18-30, 31-45, 45-60, 60-75, 75+) on how worried they are about
contracting Ebola on a scale of 1-5, where 1 is not at all worried and 5 is very worried.
i. Can ANOVA be used? Explain.
Since the explanatory variable (age group) is categorical and the response variable (level of
worry about Ebola) is also categorical (ordinal), ANOVA cannot be used here.
IF ANOVA can be used, write the null and alternative hypotheses:
ii. Ho:
iii. Ha:
2.
Exploring ANOVA Visually

Lab Activity 9 One-Way Analysis of Variance (ANOVA)

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