Please show all work be sure to bracket the p value and state if you accept or r

Question

Please show all work be sure to bracket the p value and state if you accept or reject null hypothesis Use the following information to do problems 1 and 2 below: Technician A B A plant manager, in deciding whether to purchase a machine of design A or design B, checks the times for completing a certain task on each machine. Eight technicians were used in the experiment, with each technician using both machine A and machine B in a randomized order The times (in seconds) required to complete the task are given in the accompanying table. 32 30 40 39 42 42 26 23 5 35 36 6 29 27 7 45 41 8 22 21 Machine Design Mean Completion Time (seconds) s (std dev., seconds) 33.8750 8.0965 32.3750 8 8.2451 1. Check to see if the average completion times are statistically equal or not. Use the independent design. Use the usual five step procedure at = 0.05

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  

At level of significance =    0.05          

As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    33.875          
X2 =    32.375          
              
Calculating the standard deviations of each group,              
              
s1 =    8.0965          
s2 =    8.2451          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    8          
n2 = sample size of group 2 =    8          
Thus, df = n1 + n2 - 2 =    14          
Also, sD =    4.085568906          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    0.367145931          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   2.144786688      
              
Also, using p values,              
              
p > 0.20
              
As |t| < 2.1448, and P > 0.05    WE FAIL TO REJECT THE NULL HYPOTHESIS.          

Hence, there is no significant evidence that the average completion times are not statistically equal at 0.05 level.

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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

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