Measuring the amt of contaminate in a lake. Take 64 samples from lake and find t

Question

Measuring the amt of contaminate in a lake. Take 64 samples from lake and find the mean is 81 and standard deviation is 10. Plausibly normal, no prior info, you perform a test of hypoth that the true mean is 85 against the hypoth that is less. What is the test statistic? -2.2 -2.8 -3.6 -2.9 -3.2 -4.1 Measuring the amt of contaminate in a lake. Take 64 samples from lake and find the mean is 81 and standard deviation is 10. Plausibly normal, no prior info, you perform a test of hypoth that the true mean is 85 against the hypoth that is less. What is the test statistic? -2.2 -2.8 -3.6 -2.9 -3.2 -4.1 -2.2 -2.8 -3.6 -2.9 -3.2 -4.1

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   85  
Ha:    u   <   85  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.1   ,      
alpha =    0.1          
zcrit =    -   1.281551566      
              
Getting the test statistic, as              
              
X = sample mean =    81          
uo = hypothesized mean =    85          
n = sample size =    64          
s = standard deviation =    10          
              
Thus, z = (X - uo) * sqrt(n) / s =    -3.2   [option e, answer]  
          

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