A random sample of 10 independent observations from a normal

A random sample of 10 independent observations from a normally distributed population yielded the following values 151, 153, 149, 143, 147, 146, 145, 130, 160, 152.

a) Using = .05, test the hypothesis that the true mean is 150 against the alternative that the true mean is not 150. You will calculate confidence limits to solve this problem. Show your work.

b) State the conclusion.

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   150  
Ha:    u   =/   150  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    9          
tcrit =    +/-   2.262157163      
              
Getting the test statistic, as              
              
X = sample mean =    147.6          
uo = hypothesized mean =    150          
n = sample size =    10          
s = standard deviation =    7.86271087          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.965248056          
              
              
Comparing |t| < 2.262, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

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b)

Thus, there is no significant evidence that the true mean is not 150. [CONCLUSION]