Problem
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 15 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of $9.02 \mathrm{~cm}^{3}$. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and $\bar{x}=8.08 \mathrm{~cm}^{3}$ and $\mathrm{s}=0.8 \mathrm{~cm}^{3}$. Conduct the appropriate test at the $\alpha=0.01$ level of significance. State the null and alternative hypotheses. (Type integers or decimals. Do not round.)
Solution
Step 1 ：State the null and alternative hypotheses. The null hypothesis (H0) is that the mean hippocampal volume in adolescents with alcohol use disorders is equal to the normal volume. The alternative hypothesis (H1) is that the mean hippocampal volume in adolescents with alcohol use disorders is less than the normal volume.
Step 2 ：In mathematical terms, we can express these hypotheses as follows: H0: μ = 9.02 cm³ H1: μ < 9.02 cm³ where μ represents the mean hippocampal volume in adolescents with alcohol use disorders.
Step 3 ：Final Answer: The null hypothesis is H0: μ = 9.02 cm³ and the alternative hypothesis is H1: μ < 9.02 cm³.
