Question

3) You are given the claim that the mean of a population is not equal to 24 cm. You don’t believe in this claim and so you want to test it. Suppose that you know the population standard deviation is 4 cm, and the population distribution is approximately normal. To test this claim, you take a random sample as follows X = (20, 23, 22, 24, 24, 24, 25, 26, 24, 23, 27, 24, 29, 20, 25, 26, 28). Is there enough evidence to support the claim? Justify your answer completely.

Answer 1

Ho :   µ =   24                  
Ha :   µ ╪   24       (Two tail test)          
                          
Level of Significance ,    α =    0.05                  
population std dev ,    σ =    4.0000                  
Sample Size ,   n =    17                  
Sample Mean,    x̅ = ΣX/n =    24.3529                  
                             
                          
Standard Error , SE = σ/√n =   4.0000   / √    17   =   0.9701      
Z-test statistic= (x̅ - µ )/SE = (   24.353   -   24   ) /    0.9701   =   0.36
                          

p-Value   =   0.7160   [ Excel formula =NORMSDIST(z) ]              
Decision:   p-value>α, Do not reject null hypothesis

There is not enough evidence to support the claim

THANKS

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