. Now assume that the data are from a repeated- measures study using the same sample of n = 7 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean differ- ence, and the repeated-measures t statistic. Using .05, is there a significant difference between the two sets of scores? =

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.EA: Extended Application Contagion
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#20 part b only- show full work for psych stats
20. Exercise is known to produce positive psychologi-
cal effects. Interestingly, not all exercise is equally
effective. It turns out that exercising in a natural
environment (e.g., jogging in the woods) produces
better psychological outcomes than exercising in
urban environments or in homes (Mackay & Neill,
2010). Suppose that a sports psychologist is inter-
ested in testing whether there is a difference between
exercise in nature and exercise in the lab with respect
to post-exercise anxiety levels. The researcher re-
cruits n = 7 participants who exercise in the lab and
exercise on a nature trail. The data below represent
the anxiety scores that were measured after each
exercise session.
Transcribed Image Text:20. Exercise is known to produce positive psychologi- cal effects. Interestingly, not all exercise is equally effective. It turns out that exercising in a natural environment (e.g., jogging in the woods) produces better psychological outcomes than exercising in urban environments or in homes (Mackay & Neill, 2010). Suppose that a sports psychologist is inter- ested in testing whether there is a difference between exercise in nature and exercise in the lab with respect to post-exercise anxiety levels. The researcher re- cruits n = 7 participants who exercise in the lab and exercise on a nature trail. The data below represent the anxiety scores that were measured after each exercise session.
Participant
ABCD
E
F
G
Anxiety after
Exercising
in Lab
32
3 4 5 4 59
66
52
48
52
48
52
Anxiety after
Exercising
in Nature
8
68
48
37
44
38
44
a. Treat the data as if the scores are from an indepen-
dent-measures study using two separate samples,
each with n = 7 participants. Compute the pooled
variance, the estimated standard error for the mean
difference, and the independent-measures t statistic.
Using a = .05, is there a significant difference
between the two sets of scores?
b. Now assume that the data are from a repeated-
measures study using the same sample of n = 7
participants in both treatment conditions. Compute
the variance for the sample of difference scores,
the estimated standard error for the mean differ-
ence, and the repeated-measures t statistic. Using
.05, is there a significant difference between
the two sets of scores?
α=
Transcribed Image Text:Participant ABCD E F G Anxiety after Exercising in Lab 32 3 4 5 4 59 66 52 48 52 48 52 Anxiety after Exercising in Nature 8 68 48 37 44 38 44 a. Treat the data as if the scores are from an indepen- dent-measures study using two separate samples, each with n = 7 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. Using a = .05, is there a significant difference between the two sets of scores? b. Now assume that the data are from a repeated- measures study using the same sample of n = 7 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean differ- ence, and the repeated-measures t statistic. Using .05, is there a significant difference between the two sets of scores? α=
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