The average age of a part-time seasonal employee at a Vail Resorts ski mountain

Question

The average age of a part-time seasonal employee at a Vail Resorts ski mountain has historically been 38.5 years. A random sample of 50 part-time seasonal employees in 2010 had a sample mean age of 37 years with a sample standard deviation equal to 16 years. At the 5 percent level of significance, does this sample show that the average age was different in 2010? Which is the right hypotheses to test the statement?

What are the test statistic and critical value?

Reject H0 or Do not reject H0

Write conclusion based on test result.

(Such as "There is (no) evidence ...)

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   38.5  
Ha:    u   =/   38.5  
              
As we can see, this is a    two   tailed test.      

Getting the test statistic, as              
              
X = sample mean =    37          
uo = hypothesized mean =    38.5          
n = sample size =    50          
s = standard deviation =    16          
              
Thus, z = (X - uo) * sqrt(n) / s =    -0.662912607   [ANSWER, TEST STATISTIC]
*************************
              
Thus, getting the critical z, as alpha =    0.05   ,      

alpha/2 =    0.025          

zcrit =    +/-   1.959963985   [ANSWER, CRITICAL VALUE]

***************************  
                  
As |z| < 1.95996, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Hence, there is no significant evidence that the average age was different in 2010 at 0.05 level. [CONCLUSION]      

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