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In an experiment intended to study the effect of altitude on running times, nine

ID: 3155950 • Letter: I

Question

In an experiment intended to study the effect of altitude on running times, nine professional football players were asked to run 880 yards in Oakland. California, and then again in Denver, Colorado. The times, to the nearest 1 second, for the nine athletes are given below with the Oakland time listed first. (210,225) (130,135) (190,202) (198,201) (150,156) (175,183) (280,289) (252,265) (186,193) Assuming the distribution of differences in times for running 880 yards is approximately bell shaped for professional football players, does the sample provide sufficient data to conclude mu_4 notequalto 0? Use alpha = 0.05.

Explanation / Answer

The differences are

15
5
12
3
6
8
9
13
7


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    two   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    5.178627407          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    1.726209136          
              
Calculating the mean of the differences (third column):              
              
XD =    8.666666667          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    5.020635384          
              
As df = n - 1 =    8          
              
Then the critical value of t is              
              
tcrit =    +/-   2.306004135      
              
              
Also, using p values,              
              
p =        0.001026064      
              
As t > 2.306, and P < 0.05, WE REJECT THE NULL HYPOTHESIS.          

Hence, there is sufficient evidence that ud =/= 0. [CONCLUSION]

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