Question

A baseball bat producing company wants to see if one of their brands outperforms another, Champ and Master. 10 bats of each brand are randomly selected and tested by different people to see how many hits are needed before the bat cracks or breaks. Run a hypothesis test with alpha=.05α = .05 to see how the means of the two groups compare. What can you conclude about the bats?

A B

270	364
334	302
301	350
307	348
298	396
290	325
315	342
305	359
325	327
331	355

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0                  
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   1                  
mean of sample 1,    x̅1=   307.600                  
standard deviation of sample 1,   s1 =    19.631                  
size of sample 1,    n1=   10                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   346.800                  
standard deviation of sample 2,   s2 =    25.477                  
size of sample 2,    n2=   10                  
                          
difference in sample means =    x̅1-x̅2 =    307.6000   -   346.8   =   -39.20  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    22.7425                  
std error , SE =    Sp*√(1/n1+1/n2) =    10.1708                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -39.2000   -   0   ) /    10.17   =   -3.8542
                          
Degree of freedom, DF=   n1+n2-2 =    18                  
t-critical value , t* =        2.101   (excel formula =t.inv(α/2,df)              
Decision:   | t-stat | > | critical value |, so, Reject Ho                      

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