For Questions 1-10, refer to the following information: Recreational running has taken off in recent years as a popular fitness activity. Identifying the best shoes for running has been the subject of much debate and different studies have shown different benefits to different types of shoes from barefoot running to stability shoes with large amounts of cushioning. Researchers wanted to compare knee load (a continuous measure with higher numbers indicating greater knee load) between four types of shoe types, barefoot (no shoes), minimal, neutral, and stability. Higher values of knee load may be associated with greater injury risk. A total of 200 runners of similar height and weight were included in a study and were classified by their choice of running shoe (TYPE_NEW) and measured knee load (LOAD) on a typical run. Using a 0.05 significance level, we need to determine if there is a difference in average knee load between shoe types. To do so, answer each of the following questions.

Question 1

What type of analysis is most appropriate here?(1 point)

Select one:

a. Simple linear regression

b. Multiple linear regression

c. One-way ANOVA

d. ANCOVA

e. Logistic regression

Question 2

What is the omnibus null hypothesisH0(assume 1 = barefoot, 2 = minimal, 3 = neutral, 4 = stability)?(1 point)

Select one:

a.1=2=3=4= 0

b.1=2=3=4 0

c.1=2=3=4

d.x1=x2=x3=x4

e.x1=x2=x3=x4= 0

Question 3

What is the omnibus alternative hypothesisH1(assume 1 = barefoot, 2 = minimal, 3 = neutral, 4 = stability)?(1 point)

Select one:

a.1=2=3=4 0

b. Alliare different from each other

c. At least oneiis different from the others

d.x1=x2=x3=x4 0

e. At least onexiis different from the others

For Questions 4-10, use the following excerpted SAS output: Dependent Variable: Knee load (LOAD) Source DF Sum of Squares Mean Square F Value Pr > F Model A 3062.52788 1020.84263 C <.0001 Error 196 11517.89296 B Corrected Total 199 14580.42084 R-Square Coeff Var Root MSE LOAD Mean 0.210044 36.16106 7.665818 21.19910 Source DF Type III SS Mean Square F Value Pr > F TYPE_NEW 3 3062.527877 1020.842626 17.37 <.0001 Parameter Estimate Standard Error t Value Pr > |t| Intercept 16.40683832 B 1.04318565 15.73 <.0001 TYPE_NEW Barefoot 10.26194498 B 1.48940520 6.89 <.0001 TYPE_NEW Minimal 5.88861390 B 1.46205575 4.03 <.0001 TYPE_NEW Neutral 2.50178823 B 1.62316892 1.54 0.1249 TYPE_NEW Stability 0.00000000 B . . . TYPE_NEW LOAD LSMEAN LSMEAN Number Barefoot 26.6687833 1 Minimal 22.2954522 2 Neutral 18.9086265 3 Stability 16.4068383 4 Least Squares Means for effect TYPE_NEW Pr > |t| for H0: LSMean(i)=LSMean(j) Dependent Variable: LOAD i/j 1 2 3 4 1 0.0179 <.0001 <.0001 2 0.0179 0.1560 0.0005 3 <.0001 0.1560 0.4149

Q 4

Question 4

What is the value of the model (between) degrees of freedom (labeledAabove)?(1 point)

Select one:

a. 4

b. 3

c. 200

d. 199

e. 196

Q 5

Question 5

What is the value of the error (within) mean square (labeledBabove)?(1 point)

Select one:

a. 1020.84

b. 11517.89

c. 196

d. 58.76

e. 3839.30

Q 6

Question 6

What is the value of the test statistic for the omnibus null hypothesis (labeledCabove)?(2 points)

Select one:

a. 1020.84

b. 11517.89

c. 17.37

d. 0.058

e. <0.0001

Q 7

Question 7

What is the value of the p-value for the omnibus null hypothesis test?(1 point)

Select one:

a. 0.05

b. 0.1249

c. 17.37

d. 0.058

e. <0.0001

Q 8

Question 8

What conclusion should you make regarding the omnibus null hypothesis based on the given data?(2 points)

Select one:

a. Fail to reject the omnibusand conclude there is sufficient evidence to support the claim that at least one of the mean knee loads differs from the rest.

b. Reject the omnibusand conclude there is sufficient evidence to support the claim that at least one of the mean knee loads differs from the rest.

c. Reject the omnibusand conclude there is sufficient evidence to support the claim that all of the mean knee loads differs from each other.

d. Reject the omnibusand conclude there is sufficient evidence to support the claim that all of the mean mean knee loads differs from 0.

e. Fail to reject the omnibusand conclude there is not sufficient evidence to support the claim that at least one of the mean knee loads differs from the rest.

Q 9

Question 9

Assuming youdid notreject the omnibus null hypothesis above (this may or may not be true) what would be your next steps?(1 point)

Select one:

a. Multiple comparisons tests.

b. Bonferroni test.

c. Tukey test.

d. All of the above are appropriate.

e. None of the above are appropriate.

Q 10

Question 10

Is there a reference cell for this problem? If so, what is it?(1 point)

Select one:

a. There is no reference cell.

b. Yes, the reference cell is barefoot runners.

c. Yes, the reference cell is minimal shoe runners.

d. Yes, the reference cell is neutral shoe runners.

e. Yes, the reference cell is stability shoe runners.