Use the​ t-distribution table to find the critical​ value(s) for the indicated alternative​ hypotheses, level of significance α​, and sample sizes n1 and n2. Assume that the samples are​ independent, normal, and random. Answer parts​ (a) and​ (b). Ha​: μ1≠μ2​, α=0.20​, n1=18​, n2= 8 (a) Find the critical​ value(s) assuming that the population variances are equal. ​(b) Find the critical​ value(s) assuming that the population variances are not equal.

A) find the critical value(s) assuming that the population variances are equal .   B) Find the critical value (s) assuming that they population variances are not equal.

Find the Margin of Error, if we are asked for 90% confidence interval where the mean is 52.3, the standard deviation is 2.15 and the sample size is 136.

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