Researehers wanted to measure the effect of alcohol on the development of the hi
ID: 3160120 • Letter: R
Question
Researehers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents. The researehers randomly selected 14 adolescents with alcohol use disorders. They wanted to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm^3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x =8.31 and s = 0.9. Conduct an appropriate test at the a = 0.05 level of significance. Choose the correct hypotheses. Find the test statistic.Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u >= 9.02
Ha: u < 9.02
As we can see, this is a left tailed test.
Getting the test statistic, as
X = sample mean = 8.31
uo = hypothesized mean = 9.02
n = sample size = 14
s = standard deviation = 0.9
Thus, t = (X - uo) * sqrt(n) / s = -2.951751938 [ANSWER, TEST STATISTIC]
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Other details:
Thus, getting the critical t,
df = n - 1 = 13
tcrit = - 1.770933396
Also, the p value is, as it is one tailed,
p = 0.005616986
As t < -1.771, and P < 0.05, we REJECT THE NULL HYPOTHESIS.
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