Question

Determine the appropriate critical value(s) for each of the following tests concerning the population mean: a. upper-tailed test: a = 0.10; n = 36, o = 4.0 b. lower-tailed test: a = 0.01; n = 30; s = 8.0 c. two-tailed test: a = 0.05; n = 41; s=5.7 d. two-tailed test: a = 0.20; n = 25; o = 5.2

Answer 1

In this case the hypothesis. Ho: M = Mo. , 2 , . concerning test - statistic is ze X-Mo ~ N(o,)) Ilm As n7,30 and population vavance is μηοω : It is upper-tailed test so. the coutical value is 2 = 20.10 1.28 (b). Hypothesis : Hoi Me Ho i Hi: Me Mo AS N=30 not greater than 30 and population variance is not given rather sample voorance is given. The test -statistic is t = X-Me & tn-l slon 3 crifical value for the lower failed test. 53 Fte, n-) tool, 29.5.-2.4620

(C). For this hypothesis. H. M = Mo ~ H: MIMO Here sample size n=4) 730 and sample nowance is given. By large sample theory we can say t-distribution appronimated to normale So we take erstatistic. zu HM. ~ NOOD value for the two fouled test critical is 742 = 2005/2 = 20.025 = 1.96. (1). me For this case hypothesis is as same as ( but here n = 25.430 and population variance is given. It is enough to apply Colot. Hence, we take 2-statistic. y por ~ N(0,1) critical values for the two-tailed test is 32 5. 20-20), = 20.10 = 128. Z: Da Mo
study large sample theory. And central limit theorem.