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}=8.17mathrm{cm}^3 ) and ( s = 0.8mathrm{cm}^3 ). conduct the appropriate test at the ( alpha=0.01 ) level of significance.
state the null and alternative hypotheses.
( h_0:mu )
( h_1:mu )
(typo cimals. do not round)

Explanation:

Step1: Identify the claim

The claim is that the hippocampal volumes in the alcoholic adolescents were less than the normal volume of \(9.02\ cm^{3}\).

Step2: Set up the null and alternative hypotheses

The null hypothesis \(H_{0}\) is the statement of no difference. The alternative hypothesis \(H_{1}\) is the claim we are testing.
Since we are testing if the mean is less than a certain value, for the null hypothesis \(H_{0}:\mu = 9.02\) (assuming no difference from the normal volume) and for the alternative hypothesis \(H_{1}:\mu<9.02\) (the claim that the volume is less than normal).

Answer:

\(H_{0}:\mu = 9.02\), \(H_{1}:\mu<9.02\)