Let X be the weights of newborn babies in pounds, and denote m to be its median. For a sample of 14, we have: 5.2 11.8 7.1 14.4 6.3 7.5 11.1 5.5 9.8 12.7 10.5 10.9 8.7 9.2 (a) Give point estimates of 0.25, 0.35, m, 0.75 (b) Find the following confidence intervals and, from Table II in Appendix B, state the associated confidence coefficient: i. (X(1), X(5)), a confidence interval for 0.25. ii. (X(3), X(8)), a confidence interval for 0.35. iii. (X(5), X(10)), a confidence interval for 0.5. (c) Now, we would like to test Ho: m = 8 against H₁: m < 8 at significance level α = 0.05. i. Use the sign test to test the hypothesis. ii. Use the Wilcoxon sign-rank test to test the hypothesis. iii. Use the t-test to test the hypothesis, assuming the underlying distribution is symmetric.

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