Question

In a study, researchers wanted to measure the effect of alcohol in the development of the hippocampal region in adolescents. The researchers randomly selected 26 adolescents with alcohol use disorders to compare the hippocampal volumes in the alcoholic adolescents to the normal volume of 9.08 cubic centimeters. An analysis of the sample data revealed that the hippocampal volume was distributed normally with a mean of 8.35 cm cubed and a standard deviation of 1.67 cm cubed.

a.   The researchers wanted to determine if the hippocampal values in the alcoholic adolescents were different from the normal volume of 9.08 cm cubed. Write the null and alternative hypotheses for this question. Use a t critical value of 2.06.

b.   What are the assumptions (conditions) of this test? Are the assumptions met for this sample?

c.   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.

d.   Calculate and interpret the 95% confidence interval for the test. Use a t critical of 2.06.

Answer 1

A.

H0: = 9.08

H1: 9.08

B.

Assumptions:

Simple random sample.

The population of hippocampal values is distributed normally.

C.

n = 26

= 8.35

s = 1.67

Since population std. deviation is not known, we will use the t-test.

Since the absolute value of t > t-critical i.e we can reject H0 and hence we can say that the hippocampal values in the alcoholic adolescents were different from the normal volume of 9.08.

D.

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