Eleanor Qwan is a college student who has started a non-profit organization to p

Question

Eleanor Qwan is a college student who has started a non-profit organization to provide support and companionship for elderly shut- ins. She is now at the stage of recruiting volunteers. She envisions three major tasks to be performed by volunteers: visitation clerical work, and advertisement. She is interested in whether some of these tasks would be more attractive to volunteers than other tasks, and she also is interested in whether males and females feel differently. She randomly selected 45 adult males and 45 adult females. She divided the males at random into three groups of 15 For each task, she chose a different group of males and asked each male in the group the number of hours per month he would volunteer at the task. She did the same for the females. After recording the replies, she computed the group mean for each of the six groups. These means are displayed in the graph below. 8.3 Female 7,8 7.3 Male 6.8 6.3 Visitation Clerical Advertisement work After checking that the assumptions for the test were satisfied, Eleanor performed a two-way ANOVA test. (The dependent variable was number of hours stated, and the factors were gender and task.) Her partially filled ANOVA table is shown below. Complete the table, and then answer the questions after the table. Do not round any values in the table except the Fstatistic values, which you should round to at least three decimal places.

Explanation / Answer

Gender =2

df for gender=2-1=1

df for interaction = df for gender * df for task

=1*2

df for interaction = 2

MS(Gender) = SS(Gender) / df(Gender)

=1.6/1

MS(Gender) = 1.6

MS(Interaction)=SS(Interaction) / df(interaction)

=6.95/2

MS(Interaction) = 3.475

F(Gender) = MS(Gender) / MS(Error)

=1.6/0.7957

F(Gender)=2.010

F(Interaction) = MS(Interaction) / MS(Error)

=3.475/0.7957

F(Interaction)=4.367

a)

At the significance level 0.05, the critical value of interaction F(2,84) = 3.110

b)

As the critical value for interaction is 3.110 , so both the factors affect the output.

So,

Yes, at 0.05 significance level, Eleanor can conclude that there is an interaction.

Source of variation df SS MS F Gender 1 1.6 1.6 2.010 Task 2 6.35 3.175 3.990 Interaction 2 6.95 3.475 4.367 Error 84 66.84 0.7957 Total 89 81.74

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