Sixteen undergraduate students were randomly selected from a

Sixteen undergraduate students were randomly selected from a university and their systolic blood pressure was tested. The sample mean and standard deviation were 114.6 mmHg and 10.8 mmHg respectively. Supposing that you are asked to test hypotheses H_o: µ = 120 versus H_o: µ < 120.

What is the obtained t-score for this sample under the null hypothesis?

What is the number of degrees of freedom of the obtained t-statistic?

What would be the rejection region if the level of significance is 0.05?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   120  
Ha:    u   <   120  
              
As we can see, this is a    left   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    114.6          
uo = hypothesized mean =    120          
n = sample size =    16          
s = standard deviation =    10.8          
              
Thus, t = (X - uo) * sqrt(n) / s =    -2   [ANSWER, T SCORE]

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df = n - 1 =    15   [ANSWER, DEGREES OF FREEDOM]

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Thus, getting the critical t,              

tcrit =    -   1.753050356      

Thus the rejection region is when t < -1.753. [ANSWER]