Question

Carry probabilities to at least four decimal places for intermediate steps. For extremely small probabilities, it is important to have one or two significant non-zero digits, for example, 0.000001 or 0.000034. Round off your final answer to two decimal places.

Suppose that a researcher is interested in the effect of three different diet and exercise management programs on reducing BMI (kg/m²) in young adults. The following table contains the data for the three groups:

Exercise Program I	Exercise Program II	Control Group
23.4	22.3	29.1
22.1	27.8	28.9
26.7	26.9	27.6
24.3	29.2	26.4
22.1		23.4
		27.6
		28.9

Which assumptions should be made before proceeding with a one-way analysis of variance procedure? (2 points)

Write out the null and alternative hypotheses for a one-way analysis of variance. (2 points)

Calculate the Mean Squares Between and Mean Squares Within variances. Hint: First calculate the mean and standard deviation for each group and for all the groups combined (10 points)

Calculate the F statistic. (2 points)

What is the p-value for the F statistic in question 1b? What is your conclusion about the population mean BMI among the groups? (4 points)

Answer 1

1)assumptions: all three population follows normal distribution.

all three population has equal variance.

all 3 samples are randomely taken

2) null hypohesis: all three different diet and exercise management programs have equal mean BMI reduction

altenate hypothesis:at least one diet and exercise management program have different  BMI reduction then others,

3)

applying one way ANOVA on abve:

from above  Mean Squares Between =SS(between)/df(between)=41.1728/2=20.59

Mean Squares within =SS(within)/df(witihin)=65.8066/13=5.06

3)

F statistic =MS(between)/MS(within)=20.59/5.06=4.07

4)

for above test statsitic and (2,13) degree pf freedom p value =0.0425

as p value is less than 0.05 level we reject null hypothesis

we have sufficient evidence at 0.05 level to cnclude that at least one diet and exercise management program have different  BMI reduction then others,