Question

A rods manufacturer makes rods with a length that is supposed to be 19 inches. A quality control technician sampled 21 rods and found that the sample mean length was 19.03 inches and the sample standard deviation was 0.11 inches. The technician claims that the mean rod length is more than 19 inches. What type of hypothesis test should be performed? What is the test statistic? What is the number of degrees of freedom? Does sufficient evidence exist at the α=0.1 significance level to support the technician's claim?

Answer 1

1 sample t test

Ho :   µ =   19  
Ha :   µ >   19   (Right tail test)
          
Level of Significance ,    α =    0.100  
sample std dev ,    s =    0.1100  
Sample Size ,   n =    21  
Sample Mean,    x̅ =   19.0300  
          
degree of freedom=   DF=n-1=   20  
          
Standard Error , SE = s/√n =   0.11/√21=   0.0240  
t-test statistic= (x̅ - µ )/SE =    (19.03-19)/0.024=   1.250  
          
          
p-Value   =   0.1129   [Excel formula =t.dist(t-stat,df) ]
Decision:   p-value>α, Do not reject null hypothesis       
Conclusion: There is not enough evidence to say that the mean rod length is more than 19 inches.

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