Which of the following expresses the null and alternative hypotheses for a two-tailed Bonferroni pairwise test comparing population means μ_A and μ_C?

If an ANOVA had k = 5 groups and each group had n = 8 observations, what is the total sample size N and the error degrees of freedom df used for pairwise comparisons?

You calculated t = 2.50 for a pairwise comparison with df = 18. Using a graphing calculator's TCDF method (or t-distribution), what is the two-tailed p-value approximately and how would you compute it using TCDF bounds?

In a study with k = 4 groups each with n = 20 (so N = 80), the ANOVA MSE = 4. Two group sample means are x̄₁ = 5.0 and x̄₃ = 3.0. Compute the pairwise t-statistic comparing group 1 and group 3 and give the two-tailed p-value (use df = N − k).

Complete a full Bonferroni follow-up for an ANOVA with k = 3 groups, each n = 10, N = 30, MSE = 9. Group means: A = 10, B = 12, C = 15. Perform the three pairwise comparisons (A vs B, B vs C, A vs C) by computing t-statistics, two-tailed p-values (use df = 27), applying Bonferroni correction (m = 3), and state which comparisons are significant at α = 0.05.