9. In a 2000 study in the American Journal of Psychiatry, investigators wanted t
ID: 2908760 • Letter: 9
Question
9. In a 2000 study in the American Journal of Psychiatry, investigators wanted to measure the effect of alcohol on the development of the hippocampal region of the brain (the part responsible for long term memory storage). A random sample of 12 adolescents with alcohol abuse disorders was selected. The hippocampal volume in each person was measured, resulting in 8.10 and SD s 0.70. Test whether the mean hippocampal volume in adolescents with alcohol abuse disorders is less than the typical volume of 9.02. (Assume the appropriate test may be used.)Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u > 9.02
Alternative hypothesis: u < 9.02
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.20207
DF = n - 1
D.F = 11
t = (x - u) / SE
t = 4.55
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 4.55.
Thus the P-value in this analysis is less than 0.001.
Interpret results. Since the P-value (almost 0) is less than the significance level (0.01), we can reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that the mean hippocampal volume in adolescents with alcohol abuse disorders is less than the typical volume of 9.02.
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