Question

In the 1990’s the mean song length was 240 seconds (4 minutes) long, and many believe songs are shorter in length now. A simple random sample of current 40 popular songs is obtained with sample mean 202 seconds and sample standard deviation 27 seconds. Conduct an appropriate test (classical method or P-value method) to conclude if the mean song length is less than 240 seconds at an 1% significance level. Do not use the T-test feature of your calculator.

Answer 1

Ho :   µ =   240                  
Ha :   µ <   240       (Left tail test)          
                          
Level of Significance ,    α =    0.01                  
sample std dev ,    s =    27.0000                  
Sample Size ,   n =    40                  
Sample Mean,    x̅ =   202.0000                  
                          
degree of freedom=   DF=n-1=   39                  
                          
Standard Error , SE = s/√n =   27.0000   / √    40   =   4.2691      
t-test statistic= (x̅ - µ )/SE = (   202.000   -   240   ) /    4.2691   =   -8.90
                                
                          
p-Value   =   0.0000     

Decision:   p-value<α, Reject null hypothesis

                      
Conclusion: There is enough evidence to  conclude that mean song length is less than 240 seconds    

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THANKS

revert back for doubt

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