Consider the following hypothesis test Please show your work

Consider the following hypothesis test. Please show your work so I can see how you got your answer.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   10  
Ha:    u   <   10  
              
As we can see, this is a    1   tailed test.  
              
Thus, getting the critical z, as alpha =    0.05   ,              
zcrit =    -1.644853627

Thus, rejection rule is when z < -1.645. [ANSWER, PART A]

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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   [PART B]

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Also, the p value is, using technology on the left tailed area of z = -1.9092,              
              
p =    0.028118902       [PART C]

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Comparing z and zcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.          

There is significant evidence that u < 10. [PART D]