2. In a study, researchers wanted to measure the effect of alcohol in the develo

Question

2.

In a study, researchers wanted to measure the effect of alcohol in the development of the hippocampal region in adolescents. The researchers randomly selected 12 adolescents with alcohol use disorders to compare the hippocampal volumes in the alcoholic adolescents to the normal volume of 9.02 cubic centimeters. An analysis of the sample data revealed that the hippocampal volume was distributed normally with a mean of 8.10 cm3 and a standard deviation of 1.67 cm3 (5 pts) 2. The researchers wanted to determine if the hippocampal values in the alcoholic adolescents were different from the normal volume of 9.02 cm3. Write the null and alternative hypotheses for this question. What are the assumptions (conditions) of this test? Are the assumptions met for this sample? Perform the appropriate test including the formula that you used, the calculated value of the t-statistic, and the t-critical you compared your t-statistic to using a significance level of 05. Then, state your conclusion to the test. Now suppose the researchers wanted to determine specifically if the hippocampal values in the alcoholic adolescents were less than the normal volume of 9.02 cm3. Rewrite your null and alternative hypothesis, then repeat the test and state your conclusion. a. b. c. d.

Explanation / Answer

Question 2

Part a

The null and alternative hypotheses are given as below:

Null Hypothesis: H0: Hippocampal value in the alcoholic adolescents is 9.02 cm3.

Alternative hypothesis: Ha: Hippocampal value in the alcoholic adolescents is different from 9.02 cm3.

H0: µ = 9.02 versus Ha: µ 9.02

Part b

Assumption of this test is that the given data or variable under study follows an approximately normal distribution. The condition of normality is satisfied. Observations are independent of each other. Sample size is small so that we use t distribution for this test.

Part c

Here, we have to use one sample t test for population mean.

We are given

Xbar = 8.10

S = 1.67

n = 12

df = n – 1 = 11

= 0.05

H0: µ = 9.02 versus Ha: µ 9.02

Test is two tailed.

Test statistic = t = (Xbar - µ) / [S/sqrt(n)]

Test statistic = t = (8.10 – 9.02) / [1.67/sqrt(12)]

Test statistic = t = -1.9084

Critical value = -2.2010 and 2.2010 (By using t-table)

P-value = 0.0828 (By using t-table)

P-value > = 0.05

So, we do not reject the null hypothesis.

We do not reject the null hypothesis that Hippocampal value in the alcoholic adolescents is 9.02 cm3.

There is insufficient evidence to conclude that Hippocampal value in the alcoholic adolescents is different from 9.02 cm3.

Part d

Null Hypothesis: H0: Hippocampal value in the alcoholic adolescents is 9.02 cm3.

Alternative hypothesis: Ha: Hippocampal value in the alcoholic adolescents is less than 9.02 cm3.

H0: µ = 9.02 versus Ha: µ < 9.02

We are given

Xbar = 8.10

S = 1.67

n = 12

df = n – 1 = 11

= 0.05

H0: µ = 9.02 versus Ha: µ < 9.02

Test is one tailed. (Left tailed test or lower tailed test)

Test statistic = t = (Xbar - µ) / [S/sqrt(n)]

Test statistic = t = (8.10 – 9.02) / [1.67/sqrt(12)]

Test statistic = t = -1.9084

Lower critical value = -1.7959 (by using t-table)

P-value = 0.0414

P-value < = 0.05

So, we reject the null hypothesis.

We reject the null hypothesis that Hippocampal value in the alcoholic adolescents is 9.02 cm3.

There is sufficient evidence to conclude that Hippocampal value in the alcoholic adolescents is different from 9.02 cm3.

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