Many people who work out on a regular basis think that worki

Many people who work out on a regular basis think that working out once a week is a waste of time. Ten people who started a workout program of only one workout a week. During the first week, their strength was measured by the bench press. Category 1 is the amount of weight bench pressed during week 1. Twenty four weeks later, they were measured again based on their bench press. Category 2 is the weight bench pressed during week 24. Use a repeated measures t test to determine if working out once a week is a waste of time based on bench press results. Test at the .05 level.

Participant                          1                                              2

1                                              100                                         135

2                                              250                                         240

3                                              140                                         140

4                                              175                                         190

5                                              200                                         205

6                                              125                                         150

7                                              145                                         150

8                                              175                                         180

9                                              200                                         225

10                                           110                                         135

Solution

Let

u2 = mean of week 24
u1 = initial mean

Let ud = u2 - u1.              
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 (third column):              
              
s =    13.78954369          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    4.360636595          
              
Calculating the mean of the differences (third column):              
              
XD =    13          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    2.981216095          
              
As df = n - 1 =    9          
              
Then the critical value of t is              
              
tcrit =    +   2.262157163      
              
              
Also, using p values,              
              
p =        0.00770956      
              
As t > 2.262 and P < 0.05, we Reject Ho.

Thus, there is significant evidence that the mean number of bench presses increased at 0.05 level. [CONCLUSION]