Please show your work stepbystep 41 Consider the following h

Please show your work step-by-step.

41. Consider the following hypothesis test A sample of 50 provides a sample mean of 9.46 and sample standard deviation of 2. a) At a = 0.05, what is the rejection rule? b) Compute the value of the test statistic c) What is the p-value? d) What is your conclusion?

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, the rejection rule is when z < -1.645. [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 =    1.414213562          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.7   [PART B]

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Also, the p value is, by table/technology,              
              
p =    0.003466974   [PART C]

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

Thus, there is significant evidence that u < 10. [PART D]