Fall 2023 Reagan Goostree 11/19/23 11:01 PM (?) thesis Question 3, 10.3.15-T Part 1 of 4 HW Score: $28.57 \%, 2$ of 7 points Points: 0 of 1 Save 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 10 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 $\bar{x}=8.09 \mathrm{~cm}^{3}$ and $\mathrm{s}=0.7 \mathrm{~cm}^{3}$. Conduct the appropriate test at the $\alpha=0.01$ level of significance. State the null and alternative hypotheses. \[ \begin{array}{l} \mathrm{H}_{0}: \mu \square \nabla \square \\ \mathrm{H}_{1} \mu \square \square \end{array} \] (Type integers or decimals. Do not round.)
Solution
Step 1 ：The problem is asking to state the null and alternative hypotheses for a statistical test. The null hypothesis (H0) is usually a statement of no effect or no difference. In this case, it would be that the mean hippocampal volume in adolescents with alcohol use disorders is equal to the normal volume. The alternative hypothesis (H1) is what we are testing for, in this case, it would be that the mean hippocampal volume in adolescents with alcohol use disorders is less than the normal volume.
Step 2 ：The null and alternative hypotheses are usually written in terms of population parameters, such as the population mean (μ). In this case, the null hypothesis would be \(H_{0}: \mu = 9.02\) and the alternative hypothesis would be \(H_{1}: \mu < 9.02\).
Step 3 ：Final Answer: The null hypothesis is \(\boxed{H_{0}: \mu = 9.02}\) and the alternative hypothesis is \(\boxed{H_{1}: \mu < 9.02}\)
