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 21 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm³. an analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and ( \bar{x}=8.17 mathrm{~cm}^{3} ) and ( s = 0.8 mathrm{~cm}^{3} ). conduct the appropriate test at the ( alpha=0.01 ) level of significance.

state the null and alternative hypotheses.
( h_{0}: mu=9.02 )
( h_{1}: mu<9.02 )
(type integers or decimals. do not round)

identify the t - statistic.
( t_{0}=-4.87 ) (round to two decimal places as needed)

identify the p - value
( p - value = 0.000 ) (round to three decimal places as needed)

make a conclusion regarding the hypothesis.
(

$$\begin{array}{l}\text { the null hypothesis. there } \\end{array}$$

) sufficient evidence to claim that the mean hippocampal volume is

Explanation:

Step1: <Compare P - value and significance level>

Since the significance level \(\alpha = 0.01\) and the P - value \(= 0.000\).

Step2: <Make decision based on comparison>

If \(P-\text{value}\leq\alpha\), we reject the null hypothesis \(H_0\). Here, \(0.000\leq0.01\).

Answer:

Reject the null hypothesis. There is sufficient evidence to claim that the mean hippocampal volume is less than \(9.02\mathrm{cm}^3\).