12. Choosing the appropriate test statistic You are interested in the difference between two population means. Both populations are normally distributed, and the population variances ole and 022 are known. You use an independent samples experiment to provide the data for your study. What is the appropriate test statistic? O t = in! \\/[SD2(1,11'11 + 1mg] '1.) F = 51/52 '9 2 (i1 - TQM/[512m] + 022ml] 0 F = \\/[s11;nl + 521/112] Suppose instead that the populations are not normally distributed. The test statistic given is still appropriate provided that Y You are interested in the difference between two population means. The population variances c512 and o2: are unknown and equal. You use an independent samples experiment to generate the data for your study, and each of your samples meet the large sample requirement. What is the appropriate test statistic? O t = (i1 i2}/V[Sp2(1fn1 + Unt] O F = 51/52 0 t = ram/[3,31%] O F =\\/[5211 + 532ml] Suppose instead that one (or both) of your samples does not satisfy the large sample requirement. The test statistic given is still appropriate provided that You are interested in the difference between two population means. When is it appropriate to conduct a hypothesis test using the test statistic t = (X] - X2) / V[s,2j + $2?2]? Check all that apply. The population variances of2 and o,2 are unknown, the data are generated from a matched pairs experiment, and the population of differences are normally distributed. The population variances of2 and o22 are unknown and equal, the data are generated from an independent samples experiment, and both populations are normally distributed. O The population variances o,2 and o,2 are known, the data are generated from an independent samples experiment, and both populations are normally distributed. The population variances 021 and 022 are unknown and unequal, the data are generated from an independent samples experiment, and both samples satisfy the large sample requirement. You want to compare the two population variances o12 and 022. When is it appropriate to conduct a hypothesis test using the test statistic F = s,2/s,2? Check all that apply. O The population variances o12 and o22 are unknown, and you independently sample from two normal populations. The population variances of2 and o,2 are known, and you independently sample from two normal populations. The population variances of2 and o,2 are unknown, and you independently sample from two nonnormal populations. The population variances of2 and o,2 are unknown, the samples are not independent, and the populations are not normally distributed.You are interested in comparing the central location of two populations whose data are measured on an interval scale. Your null hypothesis is that the population parameters are equal. The sample data are gathered from a matched pairs experiment. The population of differences is normally distributed. What is the appropriate test statistic? O t = (X1 - X2) / V[s,?, + $232] O t = Xp / (Sp/Vnp) O z = (X1 - X2) / V[o,2] + 0222] OF =S2/$22