Given the hypothesis Ho mu 18 Ha mu Solutiona It is a t tes

Given the hypothesis: Ho: mu 18 & Ha: mu

Solution

a)

It is a t test, as the population size is small, n = 5 < 30.

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b)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   18  
Ha:    u   <   18  
              
As we can see, this is a    left   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    17.2          
uo = hypothesized mean =    18          
n = sample size =    5          
s = standard deviation =    1.923538406          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.92998111 [ANSWER]

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c)          

Thus, getting the critical t,              
df = n - 1 =    4          
tcrit =    -   3.746947388   [ANSWER]

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d)

As |t| < 3.7469, we   FAIL TO REJECT THE NULL HYPOTHESIS.   [NO]