Question

5. Here is a list of units of toys sold by T & K over a 12month period during 2015. Were the average sales of 31 456 for 2016 significantly different from the average sales in 2015? Toy Sales in 2015 at T & K

Toy Sales in 2015 at T & K
29540
34889
34518
26764
31429
29962
31084
30506
28546
29560
29304
25852

Use α = 0.04 for your hypothesis. Use the 8-step method discussed in class to complete this study.

Answer 1

1)Ho :   µ =   31456                  
2)Ha :   µ ╪   31456       (Two tail test)          
                          
3)Level of Significance ,    α =    0.04                  

4)sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   2665.4759                  
Sample Size ,   n =    12                  
Sample Mean,    x̅ = ΣX/n =    30162.8333                  
                          
                          
Standard Error , SE = s/√n =   2665.4759   / √    12   =   769.4566      
t-test statistic= (x̅ - µ )/SE = (   30162.833   -   31456   ) /    769.4566   =   -1.681
         

5) degree of freedom=   DF=n-1=   11                  

  
6) p-Value   =   0.1210 [Excel formula =t.dist(t-stat,df) ]              
7)Decision:   p-value>α, Do not reject null hypothesis                       
8) Conclusion: There is not enough evidence that average sales of 31456 for 2016 significantly different from the average sales in 2015