(following Hogg, McKean & Craig, exercise 11.2.2) Let X1, X2, .., X10 be a random sample from a gamma distribution with a = 3 and ß = 1/0. Suppose we believe that 0 follows a gamma-distribution with a = 3 and B = 2: a) Find the posterior distribution of 0. b) If the observed x = 16.2, what is the Bayes point estimate associated with the square-error loss function? c) What is the Bayes point estimate using the mode of the posterior distribution?

Violation of which assumption below for the two-factor ANVOA is not a cause for concern with large sample sizes?     a. The populations from which the samples are selected must have equal variances.   b. The populations from which the samples are selected must be normal.   c. A violation of any assumption below would be a concern, even with large sample sizes.   d. The observations within each sample must be independent.

Question 12 In a single-factor ANOVA problem involving five populations or treatments with a random sar 37.3801. Then the value of the test statistic is O 1.619 2.316 0.432 O 1.522 O 4.248

Question 16: Please use the approporate stats table attached. Do not use a software for this problem.a. What was the observed difference between the mean PCV levels for the two groups? b.Assuming that the two groups have similar variances, estimate the standard error of the difference between the sample means c. Conduct an appropriate test to assess the difference between the two means. What do you conclude?

Question II. The following two-by-three table gives the sample proportions corresponding to different combinations of factor categories (for example, 28% of the sample fell in the cell representing category 1 of factor A and category 3 of factor B). A B .13 .19 .28 .07 .11 .22 II(a). Suppose that the sample size is n=100. Carry out a chi-squared test of independence at the 10% significance level. Make sure to state the null and alternative hypotheses, degrees of freedom, the value of your test statistic, the p-value, and the final conclusion. II(b). Now, suppose that n=1000 and repeat part 3(a). II(c). Find the smallest value of n that will result in rejection of the null hypothesis of part 3(a) at 10% level. Start by finding the appropriate x² statistic (which will depend on the n).