Please use the following information to answer questions 2a-2f:

The following data summarize the results from an independent-measures study comparing three treatment conditions.

Treatment

I II III N = 12

3 5 6 G = 60

5 5 10 X² =392

3 1 10

1 5 6

x₁ = 3 x₂ =4 x₃ = 8

T₁=12 T₂=16 T₃=32

SS₁= 8 SS₂= 12 SS₃=16

Use an ANOVA with= .05 to determine whether there are any significant differences among the three treatment means.

2a.Which of the following correctly represents the null and alternative hypothesis (MUST SHOW WORK FOR THIS PROBLEM)?

1. H_o:₁= ₂=₃

H₁: ₁=₃, but₂is different

2. H_o:_{1 2 3}

H₁:₁ =₂, but ₃ is different

3. H_o:₁=₂=₃

H₁: At least one of the treatment means is different

4. H_o:₁=₂=₃

H₁:₁₂₃

2b.Which of the followingrepresents the propercritical region(MUST SHOW WORK FOR THIS PROBLEM).

1. F=4.26

2. F=19.38

3. F=3.98

4. F=3.49

2c.Compute the test statistic(F-ratio)(MUST SHOW WORK FOR THIS PROBLEM).

Note: Must also show work for SS,df,andMS values.

2d.Based on the calculated test statistic,would you reject the null hypothesis established in question 2a(MUST SHOW WORK FOR THIS PROBLEM)?

1. yes

2. no

2e.Based on the previously conducted steps,we canconclude(MUST SHOW WORK FOR THIS PROBLEM):

1. There is not a significant difference among the three treatments.

2. At least one of the three treatments significantly differs from the others.

3. There is a significant difference between treatment condition III and the other two conditions, while there was no significant difference between treatment condition I and II.

4. There is a significant difference between treatment condition II and the other two conditions, while there was no significant difference between treatment condition I and III.

2f.Calculate²to measure the effect size for this study (MUST SHOW WORK FOR THIS PROBLEM).

Note: Leave your answer as a decimal rather than a percent.