Question

8. You may either use SPSS for this problem or carry it out using hand calculations. Women between 20-25 years of age were randomly selected, then randomly assigned to one of five fitness programs. After six weeks, the physical fitness of each woman was measured (on a scale of 0-25, with higher scores indicating higher fitness). The data are presented below and are also available in SPSS format in the “Course Documents” section of Blackboard (fitness.sav).

Fitness data

Fitness score	Fitness program
10	Anaerobic
15	Anaerobic
9	Anaerobic
7	Anaerobic
5	Anaerobic
4	Anaerobic
6	Anaerobic
9	anaerobic & flexibility
11	anaerobic & flexibility
8	anaerobic & flexibility
10	anaerobic & flexibility
7	anaerobic & flexibility
9	anaerobic & flexibility
9	anaerobic & flexibility
5	Control
7	Control
9	Control
6	Control
6	Control
3	Control
7	Control
13	Aerobic
10	Aerobic
7	Aerobic
11	Aerobic
8	Aerobic
10	Aerobic
18	Aerobic
6	aerobic & flexibility
19	aerobic & flexibility
13	aerobic & flexibility
10	aerobic & flexibility
15	aerobic & flexibility
11	aerobic & flexibility
10	aerobic & flexibility

1. Carry out a hypothesis test and construct a plot of mean values (using alpha = .05) to assess whether there is an “overall” difference among the five groups. Show all four steps of your hypothesis test.

Answer 1

Ha: at least one mean is different

TS = F = 3.848

p-value = 0.012

since p-value < alpha

we reject the null hypothesis

we conclude that there is sufficient evidence of “overall” difference among the five groups