Researchers wanted to measure the effect of alcohol on the d

Researchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolecents. The researchers randomly selected 14 adolecents with alcohol disorders. They wanted to determine whether the hippocampal volumes in the alocholic adolecents were less than the normal volume of 9.02cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x=8.48 and s=0.9. Conduct an appropriate test at the a=0.01 level of significance.

What is the correct hypothesis?

Find the test statistic. t0=___

Find the P-value: P-value=____

What conclusion can be drawn?

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   9.02  
Ha:    u   <   9.02   [ANSWER]

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b)
              
As we can see, this is a    left   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    8.48          
uo = hypothesized mean =    9.02          
n = sample size =    14          
s = standard deviation =    0.9          
              
Thus, t = (X - uo) * sqrt(n) / s =    -2.244994432 [ANSWER]

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C)

As
          
df = n - 1 =    13          

              
Thus, the p value is, as this is left tailed,              
              
p =    0.021400538   [ANSWER]

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d)      
              
As P > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.          
Thus, there is no significant evidence that the hippocampal volumes in the alocholic adolecents were less than the normal volume of 9.02cm3. [CONCLUSION]