Test the given claim Use the Pvalue method or the traditiona

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.

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 16.7 lb. Use the traditional method of testing hypotheses. 146 140 160 151 134 189 157 144 175 127 164

Solution

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 =    153.3636364          
uo = hypothesized mean =    147          
n = sample size =    11          
s = standard deviation =    16.7          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.263820007          
              
              
As |t| < 3.169, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

There is no significant evidence that these sample weights did not come from a population with a mean equal to 147 lb. [CONCLUSION]