8 Using the data shown below calculate the z value for a hyp

8. Using the data shown below, calculate the z value for a hypothesis test in which the population mean is 15 and the standard deviation is 3.

9. Is the Z you calculated in problem 8 statistically significant? Explain.

Data for questions above: 10,12,18,12,15,14,11,10,14,17,15,13,12

Solution

8.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   15  
Ha:    u   =/   15  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha/2 =    0.025          
zcrit =    +/-   1.959963985      
              
Getting the test statistic, as              
              
X = sample mean =    13.30769231          
uo = hypothesized mean =    15          
n = sample size =    13          
s = standard deviation =    3          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.033900719 [ANSWER]

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9.

As z < -1.9599, then yes, it is statistically significant at 0.05 level. [ANSWER]