Question

RReject or not reject each?

Consider the following hypotheses: | Ho: u = 1,600 HA: u 7 1,600 The population is normally distributed with a population standard deviation of 600. Compute the value of the test statistic and the resulting p-value for each of the following sample results. For each sample, determine if you can "reject/do not reject" the null hypothesis at the 10% significance level. (You may find it useful to reference the appropriate table: z table or t table) (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round "test statistic" values to 2 decimal places and "p-value" to 4 decimal places.) Test statistic p-value a. b. c. d. X = 1,740; n = 140 X = 1,740; n = 260 t = 1,450; n = 38 X = 1,550; n = 38 ( (Click to select) ( (Click to select) ( (Click to select) ( (Click to select) )

Answer 1

bon Ho: U= 1600 HAi u & 1600 The population is normally distributed with standard deviation of 600. 1. = 600 The test statistic for the above hypothesis is =JC - ll ~ N(0, 1) (a) 5c = 1740, R = 140 7x11.8322 test Steihe Z 1740 - 1600 600/5140 140 x 140 600 30 z = 82.8.254 30 = 2.76 p-value for two p-value = 0.0058 tailed test using EXCEL. command 2*(1- NORMS DIST (Z)] Here z=2.76 hooled value = 1.645 using standard das normal dist? at 10% level of significance table .. p-value (0.0058) < level of singin significance (0-10) i we reject the null hypothesis. OR Calculate value (276) > Tabulate value (1.645) we reject Ho: 4 = 1600 at to y levels of significance

6 Ž = 1740, h 260 Test statistic Z- 5-4 Sn (M-u)_1260 (1740-1600) 60o 16.1245x140 600 161245 *7 e 112.8715 30 30 - 3.7623 Test statistic Z=3.76 Calcube Tabulated Value Zon=1.645 at 10% standand level of Significance Normal dist table þ-value = 0.0002 Since p-value i we o.10 (level of sine significann. the null hypothesis. Ho: M-1600 reject © X=1450, h = 30 test statistic - 50-M 2 = ish- 530 (1450-1600) 6-1644X (-150) 600 600 - 6.1644 4 = -1.541 Test Statistic Z= -1.5414

þ- Value = 0. 1233 using Excell Command - 2*(NORIS DIST(Z)] Here 2 -1.5411 Since p-value > 0.1o. we at m to not reject the hell hy bother is y bevel of significance 5- 1550 n= 38 test statistic, oc-u) 22 on 30 (1550-1600) food - 6-16448 (-50) - 6-1644. = -0.5137 600 p- Value = 0.6075 using Excel command 200 [NORMS DISI (2) Since p-value > 0.10 Here = -0.5137 : the null hy bothest we not at Lo reject the null hy hat 7. level of significance. pejection NOTE Region is of the two-tailed form ich they brother Rejection Region Accertame region Poyecton Region DIT

6 = 1740, no 140 Test Statistic - 2.76, p-value = 0.0058, Reject to 6 C = 1740, n. 2260 Test statictic = 3.76, p-value = 0.0002 Reject to O Je = 1450 n=30 Test statistic =-1-54, p-value = 0.1233, not Reyeest Ho ( 0 - [S 5 °, 3 statistic = -0.51, p-value = 0.6075, hot Reject to