Test the given claim. Use the P-value method or the traditional method as indica

Question

Test the given claim. Use the P-value method or the traditional method as indicated. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s) or P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 12) A simple random sample of 15-year old boys from one city is obtained and their weights (in pounds) are listed below. Use a 0.01 significance level to test the claim that these sample weights come from a population with a mean equal to 147 lb. Assume that the standard deviation of the weights of all 15-year old boys in the city is known to be 16.2 lb. Use the traditional method of testing hypotheses.

Explanation / Answer

12.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   147  
Ha:    u   =/   147  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    10          
tcrit =    +/-   3.169272673      
              
Getting the test statistic, as              
              
X = sample mean =    153.0909091          
uo = hypothesized mean =    147          
n = sample size =    11          
s = standard deviation =    16.2          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.246991363          
              
As |t| < 3.169, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Hence, there is no significant evidence that the population mean from which this sample is taken is not 147 lb at 0.01 level. [CONCLUSION]

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