Question

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.
H_a: 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.
H_a: 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.
H_a: 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.
H_a: 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.
H_a: The interaction between soil condition and water amount is negligible.

H₀: The interaction is significant.
H_a: The interaction is not significant.     

H₀: There is an interaction between soil condition and water amount.
H_a: There is no interaction between soil condition and water amount.

H₀: The interaction between soil condition and water amount is negligible.
H_a: 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.

H_a: There is no interaction between ad type and question type.

H_a: There was an interaction between ad type and question type in the experiment.     

H_a: There is an interaction between ad type and question type.

H_a: There was no interaction between ad type and question type in the experiment.

Answer 1

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