A random sample of 10 observations is selected from a normal

A random sample of 10 observations is selected from a normal population. The sample mean was 19 and the sample standard deviation 3.4. Using the 0.050 significance level:

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   10  
Ha:    u   >   10  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    9          
tcrit =    +   1.833112933      

Thus,

Reject Ho if t > 1.833 [ANSWER]

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b)
              
Getting the test statistic, as              
              
X = sample mean =    19          
uo = hypothesized mean =    10          
n = sample size =    10          
s = standard deviation =    3.4          
              
Thus, t = (X - uo) * sqrt(n) / s =    8.370734983 [ANSWER, TEST STATISTIC]

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c)

REJECT HO. There is SIGNIFICANT EVIDENCE to conclude that the population mean is greater than 10.

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