Please show your work step by step Consider the following hy

Please show your work step by step.

Consider the following hypothesis test A sample of 50 provides a sample mean of 9.46 and sample variation of 4.

Solution

a)

We use a Z TEST because we have n > 30. We have n = 50 here.

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b)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   10  
Ha:    u   <   10  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    -   1.644853627      

Thus, the rejection rule is

REJECT HO IF Z < -1.6449. [ANSWER]

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C)

Getting the test statistic, as              
              
X = sample mean =    9.46          
uo = hypothesized mean =    10          
n = sample size =    50          
s = standard deviation =    2          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.909188309   [ANSWER, TEST STATISTIC]      

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D)

Also, the p value is, by table/technology,              
              
p =    0.028118902   [ANSWER]

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e)      
              
As P < 0.05, we   REJECT THE NULL HYPOTHESIS.   [CONCLUSION]