A production manager claims that the average productin of he

A production manager claims that the average productin of her employees is more than 30 an hour. A sample of 25 employyes is taken; a mean of 33 and a standards deviation of 10 is found. Test at a=0.025.

Solution

Formulating the null and alternative hypotheses,          
          
Ho:   u   =   30
Ha:    u   =/=   30
          
As we can see, this is a    1   tailed test.  
          
Thus, getting the critical t,          
df = n - 1 =    24      
tcrit =    2.063898562      
          
Getting the test statistic, as          
          
X = sample mean =    33      
uo = hypothesized mean =    30      
n = sample size =    25      
s = standard deviation =    10      
          
Thus, t = (X - uo) * sqrt(n) / s =    1.5      
          
Also, the p value is          
          
p =    0.073327823      
          
Comparing t and tcrit (or, p and significance level), we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Thus, there is no significant evidence to say that the average production is more than 30 an hour. [CONCLUSION]