Question

Use the t-distribution and the sample results to complete the test of the hypotheses. Use a 5% significance level. Assume the results come from a random sample, and if the sample size is small, assume the underlying distribution is relatively normal.

Test H0 : μ=100 vs Ha : μ<100 using the sample results x¯=91.7, s=12.5, with n=30.

Answer 1

Ho :   µ =   100                  
Ha :   µ <   100       (Left tail test)          
                          
Level of Significance ,    α =    0.05                  
sample std dev ,    s =    12.5000                  
Sample Size ,   n =    30                  
Sample Mean,    x̅ =   91.7000                  
                          
degree of freedom=   DF=n-1=   29                  
                          
Standard Error , SE = s/√n =   12.5000   / √    30   =   2.2822      
t-test statistic= (x̅ - µ )/SE = (   91.700   -   100   ) /    2.2822   =   -3.64
                             
                          
p-Value   =   0.0005   [Excel formula =t.dist(t-stat,df) ]          

   
Decision:   p-value<α, Reject null hypothesis

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