1. Fill out the following ANOVA table for the two-way ANOVA
model. This table comes from a data set with 4 levels for factor A,
3 levels for factor B, and 14 values in each group. (Round your
answer for F to two decimal places, your answers for SS and MS to
one decimal place, and the p-value to three decimal places. Do not
round any numbers until the final input into the answer
box.)
Analysis of Variance | |||||
---|---|---|---|---|---|
Source | DF | SS | MS | F | p-value |
Factor A | 316 | ||||
Factor B | 135.9 | ||||
Interaction | 78.3 | ||||
Error | |||||
Total | 4522.7 |
2. A researcher is interested in determining the ideal water and soil conditions in which to grow a species of flower that is useful to promote healthy bee colonies. Three different amounts of water and two different soil conditions are to be included in the experiment.
(a)
Identify the factors. (Select all that apply.)
amount of water
bees
flower
soil condition
(b)
Choose the correct pair of hypotheses for soil type.
H0: The mean flower growth is the same for
all soil conditions.
Ha: The mean flower growth is not the
same for all soil conditions.
H0: The mean flower growth was the same for
all the soil condition groups.
Ha: The mean flower growth for the
soil condition groups was not the
same.
H0: The mean flower growth is the same for
all soil conditions.
Ha: The mean flower growth is
different for all the levels of soil condition.
H0: The mean flower growth is not the same
for all soil conditions.
Ha: The mean flower growth is the same
for all soil conditions.
(c)
State the null and alternative hypotheses to test the interaction between soil conditions and amount of water.
H0: The interaction between soil condition
and water amount is not negligible.
Ha: The interaction between soil
condition and water amount is negligible.
H0: The interaction is significant.
Ha: The interaction is not
significant.
H0: There is an interaction between soil
condition and water amount.
Ha: There is no interaction between
soil condition and water amount.
H0: The interaction between soil condition
and water amount is negligible.
Ha: The interaction between soil
condition and water amount is not negligible.
3. A polling organization is interested in studying the effect of the way questions are worded on the types of responses they receive. They recruit volunteers and present each with one of two types of political ads: one with a "positive" message about a candidate and one with a "negative" message about the candidate's opponent. They also administer one of two different types of questions: one with an introductory clause that includes the phrase "after watching the video, how trustworthy is the candidate on a scale of 1 to 10" and the other that simply asks, "How trustworthy is the candidate on a scale of 1 to 10?"
(a)
Identify the factors. (Select all that apply.)
volunteers
type of ad
type of question
political candidate
(b)
Fill in the blank.
The type of ad has (one two three or four) levels.
(c)
Identify the alternative hypothesis to test the interaction between type of ad and type of question.
Ha: There is no interaction between ad type and question type.
Ha: There was an interaction between ad type and question type in the experiment.
Ha: There is an interaction between ad type and question type.
Ha: There was no interaction between ad type and question type in the experiment.
1)
Analysis of Variance | |||||
Source | DF | SS | MS | F | p-value |
Factor A | 3 | 316 | 105.3 | 3.83 | 0.011 |
Factor B | 2 | 135.9 | 68.0 | 2.47 | 0.088 |
Interaction | 6 | 78.3 | 13.1 | 0.47 | 0.827 |
Error | 145 | 3992.5 | 27.5 | ||
Total | 156 | 4522.7 |
1. Fill out the following ANOVA table for the two-way ANOVA model. This table comes from a data set with 4 levels for fa...
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