Final answer:
The question concerns conducting hypothesis testing including defining null and alternative hypotheses, calculating sample contrasts and their standard errors, determining test statistics and their P-values, and constructing confidence intervals for statistical analysis. However, without exact data, the calculation cannot be completed.
Step-by-step explanation:
The student's question revolves around hypothesis testing for defined contrasts in a statistical analysis scenario. The specifics include setting up null and alternative hypotheses (H0 and Ha), calculating sample contrasts (c1 and c2), determining standard errors (SE), test statistics, P-values, and constructing confidence intervals for the contrasts.
To elaborate:
- For each contrast, the null hypothesis (H0) would state that there is no difference between the groups being compared. The alternative hypothesis (Ha) would suggest a specific difference as indicated by the problem description.
- The sample contrasts (c1 and c2) are the calculated differences between group means or other statistics of interest defined in the contrasts.
- The standard errors (SEc1 and SEc2) assess the variability in the sample contrasts and are necessary to conduct hypothesis tests.
- Test statistics such as the t-statistic or F-statistic are used to assess the evidence against the null hypothesis, along with their respective P-values to determine statistical significance.
- Confidence intervals provide a range of plausible values for the population contrasts, allowing us to estimate the effect sizes with a given level of confidence (typically 95%).
Without specific sample means or additional statistics from Exercise 12.41, we cannot perform the actual calculations. However, the student is directed to use statistical principles and methods from the materials provided to execute these tasks.