Question

A researcher is interested in how music can impact exercise. She wants to know if different types of music affect how many pushups a group of adolescents can do. She randomly assigns 20 adolescents to one of three groups: control (Other usual sounds you would hear at a gym), pop music, or hip-hop. Participants listen to their respective tracks starting 2 minutes before an assistant waves their arm to begin. The research assistant counts the number of pushups each participant does. The following are the data:

Question 1 Data

Participant	Group	Number of Pushups
1	Control	13
2	Control	9
3	Control	11
4	Control	12
5	Control	21
6	Pop	19
7	Pop	18
8	Pop	25
9	Pop	32
10	Pop	29
11	Hip-hop	33
12	Hip-hop	31
13	Hip-hop	13
14	Hip-hop	20
15	Hip-hop	16

Answer the following questions for a One-way Between Subjects ANOVA:

1. What test should you run for this data and why? (Worth .5 point) **We gave you half the answer, make sure you can explain why it is this kind of test.

2. What are the populations, comparison distribution, and assumptions for this test? (Worth 1 point)

3.      What are the null and research hypotheses for this test? (Worth .5 point)

4.      What are the characteristics of the comparison distribution? (Worth 2 points)

5.      What is the critical cut-off using a p-value = .05 for a two-tailed test? (Worth .5 point)

6.      Please calculate the test statistic. Fill out the source table that is provided. (Worth 3 points)

Source	Sums of squares	Degrees of freedom	Mean Square	F-ratio
Between
Within
Total

7. What is your conclusion? (Worth 1 point)

8. How big is the effect, if there is one? (Worth 1 points)

9. If you rejected the null hypothesis, which groups are different? (Worth .5 points)

Answer 1

1) We would use ANOVA in this question because it is asked to compare three groups. We have another method to compare means of groups but those have some limitations. If we use the t-test to compare the mean of three groups considering two at a time then the Type 1 error would increase dramatically which is not a sign of good test. ANOVA is a technique to compare the means of more than two groups.

But A one-way ANOVA tells us that at least two groups are different from each other. But it won’t tell us which groups are different.

2) Here the population is Adolescence who do physical exercise and comparison groups are normally distributed.

Assumptions:

• Each group sample is drawn from a normally distributed population
• All populations have a common variance
• All samples are drawn independently of each other
• Within each sample, the observations are sampled randomly and independently of each other
• Factor effects are additive

3) H0(null hypothesis): means pushup of all groups are all equal(H₀: μ₁ = μ₂ = μ₃)

H1(alternate hypothesis): At least one of the groups is different

4) characteristics of comparison groups

5) The critical cutoff using a 5% level of significance=

3.885294

6) Test summary

7) Conclusion: Here, we can see that the F-value is greater than the F-critical value for the alpha level selected (0.05). Therefore, we have evidence to reject the null hypothesis and say that at least one of the three groups have significantly different means of the number of the pushup.

Thanks