A researcher is interested in the relationship between participation in sports (

Question

A researcher is interested in the relationship between participation in sports (# sports played) and BMI (kg/m2) in adolescents. In order to test her hypothesis, the researcher decides to divide sport participation into quartiles based on the number sports reported and includes a control group of adolescents who do not play any sports. The following incomplete ANOVA table summarizes a preliminary analysis for the difference in mean BMI for the groups. (10 points) 2) Sum of Squares Dt 54 Df Mean Square Between Groups Within Groups Total 197 42 Fill in the missing boxes in the ANOVA table above and use the space below to show your work. 1. 2. Assuming that the researcher is looking to see if there is a significant difference in BMI by level of sport participation, what would be her hypotheses? 3. Calculate the F-stat: 4. P-value (remember to use the next lowest value if exact df are not available on table 5. Conclusion:

Explanation / Answer

a)

the degrees of freedom for treatment are DFT=k1,
and the degrees of freedom for error are DFE=Nk.

The corresponding mean squares are:
MST=SST/DFT
MSE=SSE/DFE.

The test statistic, used in testing the equality of treatment means is: F=MST/MSE.

b)

Below are the null and alternate hypothesis

H0: All means are equal

H1 At least two of the means are different

c)

F=MST/MSE = 3.5874

d)

p-value = 0.0141

e)

As p-value is less than significance level of 0.05, we reject null hypothesis.

This means there are significant evidence to conclude that at least two of the means of the groups are different.

Sum of Squares Df Mean Square F Between Groups(Treatment) 54 4 13.5 3.5874 Within Groups(Error) 143 38 3.7632 Total 197 42

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