Question 4 (4.0 points) Independent random samples of m - 100 and ny - 100 observations were selected from two normal populations, Y ~ N(;o?) and Yo ~ N(;;): Population 1 Population 2 Sample mean 31 - 35.685 19 - 35.8 Sample variance 2 -0.7305 - 1.2221 (a) Find a 99% confidence interval for E(Yi ) - /1. (b) How large a sample is needed in Question 4(a) if we wish to be 95% confident that our sample mean will be within 0.12 of the true mean? (c) Suppose you wish to detect a difference between the population means. Conduct the test and state your conclusions. Use a 0.05 level of significance. Appendix: 1 I The standard normal CDF (3) - Critical values of the t-distribution V2x 1. 645 1, 960 2, 33 2, 575 0,950 0,990 0.995 P(x) 0.9500 0.9750 0. 9901 0, 9950 15 1, 753 2, 602 2, 947