Ho Null Hypothesis HA Alternative Hypothesis TS Test Static

Ho (Null Hypothesis):

H_A (Alternative Hypothesis):

TS (Test Static):

RR (Rejection Region):

Conclusion (in terms of problem):

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   500   [ANSWER]
Ha:    u   =/   500   [ANSWER]
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    495          
uo = hypothesized mean =    500          
n = sample size =    75          
s = standard deviation =    20          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.165063509   [ANSWER, TEST STATISTIC]      
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Thus, getting the critical z, as alpha =    0.1   ,      
alpha/2 =    0.05          
zcrit =    +/-   1.644853627      

Thus, the rejection region is z < -1.644853627 or z > 1.644853627. [ANSWER, REJECTION REGION]

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As |z| > 1.644853627, we   REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that the label is incorrect. [CONCLUSION]