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Data on resting and post-exercise pulse rates were collected for 8 individuals b

ID: 3133985 • Letter: D

Question

Data on resting and post-exercise pulse rates were collected for 8 individuals between 19 and 22 years of age. We wish to know if there is a difference in pre-exercise and post-exercise pulse rates. State the null and alternative statistical hypotheses for this experiment, analyze these data using the appropriate statistic, report your statistical findings, and describe your conclusions.

Individual Number

Resting

Post-exercise

1

108

112

2

60

70

3

70

78

4

54

108

5

54

64

6

72

80

7

101

108

8

96

106

Individual Number

Resting

Post-exercise

1

108

112

2

60

70

3

70

78

4

54

108

5

54

64

6

72

80

7

101

108

8

96

106

Explanation / Answer

The differences are

4
10
8
54
10
8
7
10

Formulating the null and alternative hypotheses,              
              
Ho:   ud   <=   0  
Ha:   ud   >   0  

At level of significance =    0.05          

As we can see, this is a    right   tailed test.      
              
Calculating the standard deviation of the differences
              
s =    14.7162557          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    5.202982099          
              
Calculating the mean of the differences  
              
XD =    13.875          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    2.666739907          
              
As df = n - 1 =    7          
              
Then the critical value of t is              
              
tcrit =    +   1.894578605      
              
Also, using p values,              
              
p =        0.016075652      
              
As P < 0.05, and t > 1.895, WE REJECT THE NULL HYPOTHESIS.          

Hence, there is significant evidence at 0.05 level that the post exercuse pulse rates are greater on the average than the resting pulse rates. [CONCLUSION]