Answer Happy

Q. The director of factory believes that the average time of labour spent on daily break is more than 100 mins. A sample of size 50 is tested and found that the average of labour spending as a break is 101.5 mins. From previous records it's known that the standard deviation of time spent as a daily break is o = 4 mins. (a) State the null and the alternative hypothesis. (b) With a significance of a = 0.05 test the claim on the time spent as a break.
Values of t for Selected Probabilities df = 10 0.05 0.05 t = -1.8125 0 t = 1.8125 Conf. Level One Tail Two Tails 0.1 0.45 0.9 0.98 0.01 0.02 0.99 0.005 0.01 d. f. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.1584 0.1421 0.1366 0.1338 0.1322 0.1311 0.1303 0.1297 0.1293 0.1289 0.1286 0.1283 0.1281 0.1280 0.1278 0.1277 0.1276 0.1274 0.1274 0.1273 0.1272 0.1271 0.1271 0.1270 0.1269 0.1269 0.1268 0.1268 0.1268 0.1267 0.1265 0.1263 0.1262 0.1261 0.1261 0.1260 Probabilites (Or Areas Under t-Distribution Curve) 0.3 0.5 0.7 0.8 0.9 0.95 0.35 0.25 0.15 0.1 0.05 0.025 0.7 0.5 0.3 0.2 0.1 0.05 Values oft 0.5095 1.0000 1.9626 3.0777 6.3137 12.7062 0.4447 0.8165 1.3862 1.8856 2.9200 4.3027 0.4242 0.7649 1.2498 1.6377 2.3534 3.1824 0.4142 0.7407 1.1896 1.5332 2.1318 2.7765 0.4082 0.7267 1.1558 1.4759 2.0150 2.5706 0.4043 0.7176 1.1342 1.4398 1.9432 2.4469 0.4015 0.7111 1.1192 1.4149 1.8946 2.3646 0.3995 0.7064 1.1081 1.3968 1.8595 2.3060 0.3979 0.7027 1.0997 1.3830 1.8331 2.2622 0.3966 0.6998 1.0931 1.3722 1.8125 2.2281 0.3956 0.6974 1.0877 1.3634 1.7959 2.2010 0.3947 0.6955 1.0832 1.3562 1.7823 2.1788 0.3940 0.6938 1.0795 1.3502 1.7709 2.1604 0.3933 0.6924 1.0763 1.3450 1.7613 2.1448 0.3928 0.6912 1.0735 1.3406 1.7531 2.1315 0.3923 0.6901 1.0711 1.3368 1.7459 2.1199 0.3919 0.6892 1.0690 1.3334 1.7396 2.1098 0.3915 0.6884 1.0672 1.3304 1.7341 2.1009 0.3912 0.6876 1.0655 1.3277 1.7291 2.0930 0.3909 0.6870 1.0640 1.3253 1.7247 2.0860 0.3906 0.6864 1.0627 1.3232 1.7207 2.0796 0.3904 0.6858 1.0614 1.3212 1.7171 2.0739 0.3902 0.6853 1.0603 1.3195 1.7139 2.0687 0.3900 0.6848 1.0593 1.3178 1.7109 2.0639 0.3898 0.6844 1.0584 1.3163 1.7081 2.0595 0.3896 0.6840 1.0575 1.3150 1.7056 2.0555 0.3894 0.6837 1.0567 1.3137 1.7033 2.0518 0.3893 0.6834 1.0560 1.3125 1.7011 2.0484 0.3892 0.6830 1.0553 1.3114 1.6991 2.0452 0.3890 0.6828 1.0547 1.3104 1.6973 2.0423 0.3881 0.6807 1.0500 1.3031 1.6839 2.0211 0.3875 0.6794 1.0473 1.2987 1.6759 2.0086 0.3872 0.6786 1.0455 1.2958 1.6706 2.0003 0.3869 0.6780 1.0442 1.2938 1.6669 1.9944 0.3867 0.6776 1.0432 1.2922 1.6641 1.9901 0.3866 0.6772 1.0424 1.2910 1.6620 1.9867 31.8210 6.9645 4.5407 3.7469 3.3649 3.1427 2.9979 2.8965 2.8214 2.7638 2.7181 2.6810 2.6503 2.6245 2.6025 2.5835 2.5669 2.5524 2.5395 2.5280 2.5176 2.5083 2.4999 2.4922 2.4851 2.4786 2.4727 2.4671 2.4620 2.4573 2.4233 2.4033 2.3901 2.3808 2.3739 2.3685 63.6559 9.9250 5.8408 4.6041 4.0321 3.7074 3.4995 3.3554 3.2498 3.1693 3.1058 3.0545 3.0123 2.9768 2.9467 2.9208 2.8982 2.8784 2.8609 2.8453 2.8314 2.8188 2.8073 2.7970 2.7874 2.7787 2.7707 2.7633 2.7564 2.7500 2.7045 2.6778 2.6603 2.6479 2.6387 2.6316 26 27 28 29 30 40 50 60 70 80 90 Arn
90 100 250 500 0.1260 0.1260 0.1258 0.1257 0.3866 0.3864 0.3858 0.3855 0.6772 0.6770 0.6755 0.6750 1.0424 1.0418 1.0386 1.0375 1.2910 1.2901 1.2849 1.2832 1.6620 1.6602 1.6510 1.6479 1.9867 1.9840 1.9695 1.9647 2.3685 2.3642 2.3414 2.3338 2.6316 2.6259 2.5956 2.5857 了 0.1257 0.3853 0.6745 1.0364 1.2816 1.6449 1.9600 2.3263 2.5758
Standard Normal Distribution Table 0.3944 Z z= 1.25 Z 0 0.01 0.02 0.04 0.05 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 0.0000 0.0398 0.0793 0.1179 0.1554 0.1915 0.2257 0.2580 0.2881 0.3159 0.3413 0.3643 0.3849 0.4032 0.4192 0.4332 0.4452 0.4554 0.4641 0.4713 0.4772 0.4821 0.4861 0.4893 0.4918 0.4938 0.4953 0.4965 0.4974 0.4981 0.4987 0.0040 0.0438 0.0832 0.1217 0.1591 0.1950 0.2291 0.2611 0.2910 0.3186 0.3438 0.3665 0.3869 0.4049 0.4207 0.4345 0.4463 0.4564 0.4649 0.4719 0.4778 0.4826 0.4864 0.4896 0.4920 0.4940 0.4955 0.4966 0.4975 0.4982 0.4987 0.0080 0.0478 0.0871 0.1255 0.1628 0.1985 0.2324 0.2642 0.2939 0.3212 0.3461 0.3686 0.3888 0.4066 0.4222 0.4357 0.4474 0.4573 0.4656 0.4726 0.4783 0.4830 0.4868 0.4898 0.4922 0.4941 0.4956 0.4967 0.4976 0.4982 0.4987 0.03 0.0120 0.0517 0.0910 0.1293 0.1664 0.2019 0.2357 0.2673 0.2967 0.3238 0.3485 0.3708 0.3907 0.4082 0.4236 0.4370 0.4484 0.4582 0.4664 0.4732 0.4788 0.4834 0.4871 0.4901 0.4925 0.4943 0.4957 0.4968 0.4977 0.4983 0.4988 0.0160 0.0557 0.0948 0.1331 0.1700 0.2054 0.2389 0.2704 0.2995 0.3264 0.3508 0.3729 0.3925 0.4099 0.4251 0.4382 0.4495 0.4591 0.4671 0.4738 0.4793 0.4838 0.4875 0.4904 0.4927 0.4945 0.4959 0.4969 0.4977 0.4984 0.4988 0.0199 0.0596 0.0987 0.1368 0.1736 0.2088 0.2422 0.2734 0.3023 0.3289 0.3531 0.3749 0.3944 0.4115 0.4265 0.4394 0.4505 0.4599 0.4678 0.4744 0.4798 0.4842 0.4878 0.4906 0.4929 0.4946 0.4960 0.4970 0.4978 0.4984 0.4989 0.06 0.0239 0.0636 0.1026 0.1406 0.1772 0.2123 0.2454 0.2764 0.3051 0.3315 0.3554 0.3770 0.3962 0.4131 0.4279 0.4406 0.4515 0.4608 0.4686 0.4750 0.4803 0.4846 0.4881 0.4909 0.4931 0.4948 0.4961 0.4971 0.4979 0.4985 0.4989 0.0279 0.0675 0.1064 0.1443 0.1808 0.2157 0.2486 0.2794 0.3078 0.3340 0.3577 0.3790 0.3980 0.4147 0.4292 0.4418 0.4525 0.4616 0.4693 0.4756 0.4808 0.4850 0.4884 0.4911 0.4932 0.4949 0.4962 0.4972 0.4979 0.4985 0.4989 0.0319 0.0714 0.1103 0.1480 0.1844 0.2190 0.2517 0.2823 0.3106 0.3365 0.3599 0.3810 0.3997 0.4162 0.4306 0.4429 0.4535 0.4625 0.4699 0.4761 0.4812 0.4854 0.4887 0.4913 0.4934 0.4951 0.4963 0.4973 0.4980 0.4986 0.4990 0.0359 0.0753 0.1141 0.1517 0.1879 0.2224 0.2549 0.2852 0.3133 0.3389 0.3621 0.3830 0.4015 0.4177 0.4319 0.4441 0.4545 0.4633 0.4706 0.4767 0.4817 0.4857 0.4890 0.4916 0.4936 0.4952 0.4964 0.4974 0.4981 0.4986 0.4990