3. Some sports psychologists believe that an athlete's motivation is related to how many hours they will devote to training in a 2-week period. To see if this is true, a sports trainer measures the motivation (M) and training hours (TH) of a random sample of 8 Olympic-class athletes and obtains the following data: M TH 57 40 74 46 42 38 48 36 75 54 62 42 665 76 550 69 25 a) Is there a significant correlation between M and TH in this sample (a≤.05)? (8 points) b) If another athlete obtained an M score of 70, what would his or her predicted TH score be and what are the 90% bounds to the error of this prediction? (10 points)

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3. Some sports psychologists believe that an athlete's
motivation is related to how many hours they will devote to
training in a 2-week period. To see if this is true, a sports
trainer measures the motivation (M) and training hours
(TH) of a random sample of 8 Olympic-class athletes and
obtains the following data:
M
TH
57
40
74
46
42
38
48
36
75
54
62
42
665
76
550
69
25
a) Is there a significant correlation between M and TH in this
sample (a≤.05)? (8 points)
b) If another athlete obtained an M score of 70, what would his
or her predicted TH score be and what are the 90% bounds to
the error of this prediction? (10 points)
Transcribed Image Text:3. Some sports psychologists believe that an athlete's motivation is related to how many hours they will devote to training in a 2-week period. To see if this is true, a sports trainer measures the motivation (M) and training hours (TH) of a random sample of 8 Olympic-class athletes and obtains the following data: M TH 57 40 74 46 42 38 48 36 75 54 62 42 665 76 550 69 25 a) Is there a significant correlation between M and TH in this sample (a≤.05)? (8 points) b) If another athlete obtained an M score of 70, what would his or her predicted TH score be and what are the 90% bounds to the error of this prediction? (10 points)
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