Question

A light bulb manufacturer guaran tees that the mean life of a certain type of light bulb is at least 750 hours. A random sample of 250 light bulbs has a mean life of 745 hours. The population standard deviation standard deviation is 60 hours. Test the manufacturer's claim is at  .

a) Write the null and alternative hypotheses and tell which is the claim.

b) Write the P-value and how you calculated it. (what you typed into the calculator)

c) Write a sentence interpreting the decision.

Answer 1

Ho :   µ =   750                  
Ha :   µ >   750       (Right tail test)          
                          
Level of Significance ,    α =    0.05                  
population std dev ,    σ =    60.0000                  
Sample Size ,   n =    250                  
Sample Mean,    x̅ =   745.0000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   60.0000   / √    250   =   3.7947      
Z-test statistic= (x̅ - µ )/SE = (   745.000   -   750   ) /    3.7947   =   -1.32
                                
                          
p-Value   =   0.9062   [ Excel formula =NORMSDIST(z) ]              
Decision:   p-value>α, Do not reject null hypothesis                       
Conclusion: There is not enough evidence to conclude that  mean life of a certain type of light bulb is at least 750 hours

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