Question

In a​ study, researchers wanted to measure the effect of alcohol on the hippocampal​ region, the portion of the brain responsible for​ long-term memory​ storage, in adolescents. The researchers randomly selected

1010

adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of

9.029.02

cm cubedcm3.

An analysis of the sample data revealed that the hippocampal volume is approximately normal with x overbar=8.0cm3 and s=0.7cm3. Conduct the appropriate test at the alphaαequals=0.01 level of significance.

a)State the null and alternative hypotheses.

b) T-statistic= ___

c) P-value=___

d) Make a conclusion regarding the hypothesis.

Answer 1

a)

H0: >= 9.02

Ha: < 9.02

b)

Test statistics

t = - / S / sqrt(n)

= 8 - 9.02 / 0.7 / sqrt(10)

= -4.61

c)

Using T table,

With test statistics t = -4.61 and df = 9

p-value = 0.0006

D)

Since p-value < 0.01 level, we have sufficient evidence to reject the null hypothesis.

we conclude at 0.01 level that we have enough evidence to support the claim that the hippocampal volumes in the

alcoholic adolescents were less than the normal volume of 9.02 cm³