Question

Suppose that National Motors randomly selects a sample of n = 91 ZX-900s. The company records the stopping distance of each of these automobiles and calculates the mean and standard deviation of the sample of n = 81 stopping distances to be ȳ = 57.8feet and s = 6.02feet.

1. Conduct hypothesis test

H0 :μ=60, Ha :μ<60.

Set α = 0.5. And calculate the p-value.

Answer 1

Ho :   µ =   60                  
Ha :   µ <   60       (Left tail test)          
                          
Level of Significance ,    α =    0.05                  
sample std dev ,    s =    6.0200                  
Sample Size ,   n =    81                  
Sample Mean,    x̅ =   57.8000                  
                          
degree of freedom=   DF=n-1=   80                  
                          
Standard Error , SE = s/√n =   6.0200   / √    81   =   0.6689      
t-test statistic= (x̅ - µ )/SE = (   57.800   -   60   ) /    0.669   =   -3.29
                          
  
p-Value   =   0.0007   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value<α, Reject null hypothesis                       
Conclusion: There is enough evidence to conclude that true mean is less than 60