Question

Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (−) in seconds per week. Picture Click here for the Excel Data File −0.16 −0.15 −0.20 −0.17 +0.26 −0.19 +0.30 +0.43 −0.10 −0.31 −0.48 −0.44 −0.51 −0.67 −0.05 −0.24 −0.51 +0.05

State the null hypothesis and the alternate hypothesis.

State the decision rule for 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.05 significance level.

Estimate the p-value.

Answer 1

Ho :   µ =   0                  
Ha :   µ ╪   0       (Two tail test)          
                          
Level of Significance ,    α =    0.05                  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   0.2980                  
Sample Size ,   n =    18                  
Sample Mean,    x̅ = ΣX/n =    -0.1744                  
                          
degree of freedom=   DF=n-1=   17                  
                          
Standard Error , SE = s/√n =   0.2980   / √    18   =   0.0702      
t-test statistic= (x̅ - µ )/SE = (   -0.174   -   0   ) /    0.0702   =   -2.484
                             
                          
p-Value   =   0.0237   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value<α, Reject null hypothesis                       
Conclusion: There is enough evidence that mean gain/loss time is not zero and different than zero.

  

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