A few years back, a coffee company tried to market drinking coffee as a way to r
ID: 3291092 • Letter: A
Question
A few years back, a coffee company tried to market drinking coffee as a way to relax-and they weren't talking about decaf. Jon decided to test this. He randomly selected six adults. He recorded their heart rates, then recorded them again half an hour after each person drank two cups of regular coffee. His data are shown at right. The data are paired, because each person (experimental unit) gives you two numbers, Before and After: because each After is associated with one specific Before, and because you can't rearrange Before or After and still have the data make sense. Jon selected the 0.01 significance level. (Ho tests for difference even though he believes coffee increases heart rate, because it could decrease it.) Person Before After 1 78 83 2 64 66 3 70 77 4 71 74 5 70 75 6 68 71Explanation / Answer
Person
Before
After
Di
(Di-D)
(Di-D)^2
1
78
83
5
0.833333333
0.694444444
2
64
66
2
-2.166666667
4.694444444
3
70
77
7
2.833333333
8.027777778
4
71
74
3
-1.166666667
1.361111111
5
70
75
5
0.833333333
0.694444444
6
68
71
3
-1.166666667
1.361111111
16.83333333
H0: D = 0
H1: D ¹ 0
D=EDi/n
=25/6
=4.167
S=E(Di-D)^2/n-1
=16.83/6
=1.67
tSTAT=D-m/SD/n
=4.167-0/1.67/6
=6.11
tCRIT is +-4.03. tSTAT > tCRIT. Hence, reject the null hypothesis.
Person
Before
After
Di
(Di-D)
(Di-D)^2
1
78
83
5
0.833333333
0.694444444
2
64
66
2
-2.166666667
4.694444444
3
70
77
7
2.833333333
8.027777778
4
71
74
3
-1.166666667
1.361111111
5
70
75
5
0.833333333
0.694444444
6
68
71
3
-1.166666667
1.361111111
16.83333333
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