A nutritionist randomly selected 16 bicyclists and divided into three groups. There were 6, 5 and 5 bicyclists in groups 1, 2 and 3, respectively. Members of the first group were given vitamin supplements to take with each of their meals over the next 3 weeks. The second group was instructed to eat a particular type of high-fiber whole-grain cereal for the next 3 weeks. Members of the third group were instructed to eat as they normally do. After the 3-week period elapsed, each bicyclist was required to ride 6 miles. The following times were recorded: Vitamin group 16.2 16.0 17.0 15.2 15.6 15.4 Fiber cereal group 15.1 16.3 15.8 16.4 16.0 Control group 17.9 17.2 16.4 16.6 16.8 Do the data provide sufficient evidence, at the 5 percent level of significance, to conclude that the average times for the 6-mile ride are the same for these three groups? (Give H0, Ha, observed test statistic, P-value, decision and conclusion.) If the three average times are not the same, then identify the group that is different from the other two.
[10] A nutritionist randomly selected 16 bicyclists and divided into three groups. There
were 6, 5 and 5 bicyclists in groups 1, 2 and 3, respectively. Members of the first group
were given vitamin supplements to take with each of their meals over the next 3 weeks.
The second group was instructed to eat a particular type of high-fiber whole-grain cereal
for the next 3 weeks. Members of the third group were instructed to eat as they normally
do. After the 3-week period elapsed, each bicyclist was required to ride 6 miles. The following times were recorded:
Vitamin group 16.2 16.0 17.0 15.2 15.6 15.4
Fiber cereal group 15.1 16.3 15.8 16.4 16.0
Control group 17.9 17.2 16.4 16.6 16.8
Do the data provide sufficient evidence, at the 5 percent level of significance, to conclude that the average times for the 6-mile ride are the same for these three groups? (Give H0, Ha, observed test statistic, P-value, decision and conclusion.) If the three average times are not the same, then identify the group that is different from the other two.
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