A. Let x1, X2, ... Xn and y1, y2, Ym be independent random samples from two normal distributions N(H1,02) and N(uz,02), respectively, where a2 is the common variance. If 4, and uz are unknown. We wish to construct a likelihood ratio test of Ho: o? = o against HA: o? = o, assuming that of > of. %3D

Do a two-sample test for equality of means assuming unequal variances. Calculate the p-value using Excel. (a-1) Comparison of GPA for randomly chosen college juniors and seniors: x⎯⎯1x¯1 = 4.5, s1 = .20, n1 = 15, x⎯⎯2x¯2 = 4.9, s2 = .30, n2 = 15, α = .025, left-tailed test.(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)        d.f. Not attempted t-calculated Not attempted p-value Not attempted t-critical Not attempted    (a-2) Based on the above data choose the correct decision.   Do not reject the null hypothesis Reject the null hypothesis

The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers?                                                                                                                                                                                                                                                                    Use α = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal.   Teacher 1 Teacher 2 ?̅1 =  473 ?̅2 = 459 S1 = 39.7 S2 = 24.5 n 1 = 8 n 2 = 18   a. State the null and alternate hypotheses (write it mathematically) and write your claim.   b. Find the test statistic        c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and…

Please note the question is: What is the distribution of the t-test statistic if m, n -----> ∞ ?