Homework SourseIn a study published in the American Journal of Psychiatry r
In a study published in the American Journal of Psychiatry, researchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents. The hippocampus is the portion of the brain responsible for long-term memory storage. The researchers randomly selected 13 subjects with adolescent-onset alcohol use disorders to test the claim that hippocampal volumes in alcoholic adolescents were less than the normal volume of 9.02 cubic centimeters. An analysis of the sample data revealed that the hippocampal volume is approximately normal with mean 8.26 and standard deviation=.08. Use the .05 level of significance.
a. State the null and the alternate hypotheses. Ho: ______ and Ha: ______
b. State the critical value(s) for this test. ___
c. Find the test statistic. ___
d. Approximate the p-value for this test. _____
e. State your conclusion in the context of this problem____
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.
Thus, getting the critical t,
df = n - 1 = 12
tcrit = -1.782287556 [ANSWER, CRITICAL VALUE]
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C)
Getting the test statistic, as
X = sample mean = 8.26
uo = hypothesized mean = 9.02
n = sample size = 13
s = standard deviation = 0.08
Thus, t = (X - uo) * sqrt(n) / s = -34.25273712 [ANSWER, TEST STATISTIC]
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d)
Also, the p value is, using technology,
p = 0.000000000000122012 [ANSWER]
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E)
As t < -1.7823, then we REJECT THE NULL HYPOTHESIS.
Thus, there is significant evidence that hippocampal volumes in alcoholic adolescents were less than the normal volume of 9.02 cubic centimeters. [CONCLUSION]
