In a study published in the American Journal of Psychiatry (157:737–744, May 2000), researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 12 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cubic centimeters (cm3). An analysis of the sample data revealed that the hippocampal volume is approximately normal with sample mean=8.10 cm3 and s=0.7 cm3. Conduct the appropriate test at α=0.01 level of significance.
We have here,
Sample mean = 8.10 cm3
Sample standard deviation = 0.7 cm3
Sample size =12,
Population mean = 9.02 cm3
Degree of freedom =n-1 = 12 -1 = 11
We can use here t test statistic formula is
P value is 0.0004 ..................by using TDIST(-4.55,11,1)
P value is 0.0004<0.01
Therefore, we reject H0.
Conclusion : We have sufficient evidence at α=0.01 level of significance that, the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cubic centimeters (cm3).
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