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.

Consider the following hypothesis test. Ha: #15 A sample of 50 gives a sample mean of 14.2 and sample variance of 25. 0.05, what is the rejection rule? a) At b) Compute the value of the test statistic c) What is the p-value? d) What is your conclusion? What is your conclusion?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   15  
Ha:    u   =/=   15  
              
As we can see, this is a    2   tailed test.      
              
Thus, getting the critical z, as alpha = 0.05, using table/technology,                          
zcrit =    1.959963985          

Hence, the rejection rule is when z < -1.96 or z > 1.96. [ANSWER]          

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Getting the test statistic, as              
              
X = sample mean =    14.2          
uo = hypothesized mean =    15          
n = sample size =    50          
s = standard deviation =    5          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.13137085 [ANSWER, PART B]

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Also, the p value is, by using technology,              
          
p =    0.257899035   [ANSWER, PART C]

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

Thus, there is no signficant evidence that the mean is not 15. [PART D]