Question

Maria believes that the average running time of movies is equal to 160 minutes. A sample of 5 movies was taken and the following running times were obtained , 150,155,165,170,185. Assume the population of the running times is normally distributed. Find the p-value at the 95% level of significance

Answer 1

Ho :   µ =   160  
Ha :   µ ╪   160   (Two tail test)
          
Level of Significance ,    α =    0.050  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   13.6931  
Sample Size ,   n =    5  
Sample Mean,    x̅ = ΣX/n =    165.0000  
          
degree of freedom=   DF=n-1=   4  
          
Standard Error , SE = s/√n =   13.6931/√5=   6.1237  
t-test statistic= (x̅ - µ )/SE =    (165-160)/6.1237=   0.8165  
          

          
p-Value   =   0.4601   [Excel formula =t.dist.2t(t-stat,df) ]
Decision:   p-value>α, Do not reject null hypothesis