\[ \bar{x}_{O}=\text { i } 34.69 \] (c) To measure the effect size of the young blood, we are interested in the difference in means \( \bar{x}_{Y}-\bar{x}_{O} \). What is this differe \[ \bar{x}_{Y}-\bar{x}_{O}=\mathbf{i}^{27.37} \] (d) Does this data come from an experiment or an observational study? \( \square \) (e) If the difference is found to be significant, can we conclude that young blood increases exercise endurance in old mice? (F are just beginning to start similar studies on humans.) \( \square \) \( { }^{1} \) Sanders L., "Young blood proven good for old brain", Science News, 185(11), May 31, 2014. \( { }^{2} \) Manishas, et al. "Restoring Systemic GDF11 Levels Reverses Age-Related Dysfunction in Mouse Skeletal Muscle", Science

Sure, let's address each part of your question step by step. --- **(c) Calculating the Difference in Means \( \bar{x}_{Y} - \bar{x}_{O} \)** Given: - Mean exercise endurance for **Old** mice (\( \bar{x}_{O} \)) = **34.69** - Mean exercise endurance for **Young** mice (\( \bar{x}_{Y} \)) = **62.06** (assuming from context; adjust if different) The difference in means is calculated as: \[ \bar{x}_{Y} - \bar{x}_{O} = 62.06 - 34.69 = 27.37 \] **Answer:** The difference in means is **27.37**. --- **(d) Determining the Study Design: Experiment or Observational Study?** **Explanation:** - **Experiment:** Involves the researcher actively manipulating one or more variables to observe the effect on another variable. It typically includes random assignment to treatment and control groups. - **Observational Study:** Involves observing subjects in a natural setting without any manipulation by the researcher. **Context of the Study:** - The study involves administering young blood to old mice to observe its effect on exercise endurance. - This involves **active manipulation** (injecting young blood) and likely includes control groups for comparison. **Answer:** This data comes from an **experiment**. --- **(e) Interpreting the Significance of the Difference** **Question:** If the difference is found to be significant, can we conclude that young blood increases exercise endurance in old mice? **Explanation:** - **Statistical Significance:** Indicates that the observed effect is likely not due to random chance. - **Causation vs. Correlation:** Since this is an experimental study with controlled manipulation of the independent variable (young blood), we can infer a causal relationship, provided the study is well-designed and other confounding factors are controlled. **Considerations:** - Ensure that the experiment had proper randomization, control groups, and sufficient sample size. - Replicability of results strengthens the conclusion. - While the results may be promising, further studies (especially in humans) are necessary to generalize the findings. **Answer:** **Yes**, if the difference is statistically significant, we can conclude that **young blood increases exercise endurance in old mice** based on this experimental data. --- **References:** 1. Sanders L., "Young blood proven good for old brain", *Science News*, 185(11), May 31, 2014. 2. Manishas, et al. "Restoring Systemic GDF11 Levels Reverses Age-Related Dysfunction in Mouse Skeletal Muscle", *Science*. --- Feel free to ask if you need further clarification on any of these points!