Many studies have suggested that there is a link between exercise and healthy bo
ID: 3220427 • Letter: M
Question
Many studies have suggested that there is a link between exercise and healthy bones. Exercise stresses the bones and this causes them to get stronger. One study examined the effect of jumping on the bone density of growing rats. There were three treatments: a control with no jumping, a low-jump condition (the jump height was 30 centimeters), and a high-jump condition (60 centimeters). After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats (expressed in mg/cm3 ) was measured. Here are the data. data84.dat
Here is the data. it is ogranized in obs, the group, g, and density. then it starts over every four words.
obs, group, g, density: 1 Control 1 565 2 Control 1 628 3 Control 1 601 4 Control 1 619 5 Control 1 596 6 Control 1 527 7 Control 1 642 8 Control 1 612 9 Control 1 587 10 Control 1 651 11 Lowjump 2 709 12 Lowjump 2 626 13 Lowjump 2 628 14 Lowjump 2 629 15 Lowjump 2 622 16 Lowjump 2 620 17 Lowjump 2 651 18 Lowjump 2 626 19 Lowjump 2 647 20 Lowjump 2 621 21 Highjump 3 585 22 Highjump 3 595 23 Highjump 3 624 24 Highjump 3 620 25 Highjump 3 582 26 Highjump 3 601 27 Highjump 3 640 28 Highjump 3 627 29 Highjump 3 617 30 Highjump 3 628
Please fill in all the empty boxes
(b) Run the analysis of variance. Report the F statistic with its degrees of freedom and P-value. What do you conclude? (Round your test statistic to two decimal places and your P-value to three decimal places.)
Group n s Control Low jump High jumpExplanation / Answer
Answer:
Many studies have suggested that there is a link between exercise and healthy bones. Exercise stresses the bones and this causes them to get stronger. One study examined the effect of jumping on the bone density of growing rats. There were three treatments: a control with no jumping, a low-jump condition (the jump height was 30 centimeters), and a high-jump condition (60 centimeters). After 8 weeks of 10 jumps per day, 5 days per week, the bone density of the rats (expressed in mg/cm3 ) was measured. Here are the data. data84.dat
(a) Make a table giving the sample size, mean, and standard deviation for each group of rats. Consider whether or not it is reasonable to pool the variances. (Round your answers for x, s, and to one decimal place.)
Please fill in all the empty boxes
n
Mean
Std. Dev
standard error
Control
10
602.8
37.0
11.7
Lowjump
10
637.9
27.1
8.6
Highjump
10
611.9
19.8
6.3
Since Sample sizes are equal, we can pool the variances.
(b) Run the analysis of variance. Report the F statistic with its degrees of freedom and P-value. What do you conclude? (Round your test statistic to two decimal places and your P-value to three decimal places.)
F
= 3.98
P
=0.030
Calculated F=3.98, P=0.030 < 0.05 level. Ho is rejected.
There is significant difference among the three groups.
ANOVA table
Source
SS
df
MS
F
p-value
Treatment
6,636.07
2
3,318.033
3.98
.0304
Error
22,481.40
27
832.644
Total
29,117.47
29
n
Mean
Std. Dev
standard error
Control
10
602.8
37.0
11.7
Lowjump
10
637.9
27.1
8.6
Highjump
10
611.9
19.8
6.3