- Question 5 Historically The Average Time A Customer Takes With A Teller At A Particular Bank Was 130 Seconds To Determ 1 (138.28 KiB) Viewed 54 times
attached z-table only for the calculation. Thank you!
QUESTION 5 Historically, the average time a customer takes with a teller at a particular bank was 130 seconds. To determine whether the average time with the teller had changed since they changed the staff manager, the bank undertook a random sample of the waiting time (in seconds) recorded by 15 customers. The results are in the X2 column of the data file P14.12.xls which can be found in a folder under the CML Quizzes tab. Assume that the test is performed at the 5% level of significance and that the distribution of waiting times is approximately normally distributed. 1. State the direction of the alternative hypothesis used to test whether average waiting time had changed. Type gt (greater than), ge (greater than or equal to), It (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box. 2. Calculate the test statistic correct to three decimal places (hint: use Descriptive Statistics to calculated the standard deviation and sample mean). 3. By referring to the appropriate Z or t-table, which of the following four given numbers is most likely to be the actual p-value for the test? Namely, 0.1650, 0.4292, 0.0708, or 0.7213. Enter your chosen number as your answer, using all four decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. Regardless of your answer for 4, if the null hypothesis was rejected, could we conclude that the average time is not 130 seconds at the 5% level of significance? Type yes or no.
TABLE A.5 Areas of the standard normal distributionu = 0,o=1 The entries in this table are the probabilities that a standard normal random variable is between 0 and 21 (the shaded area). Z 0 21 21 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 .0040 .0438 .0832 .1217 .1591 .0120 .0517 .0910 .1293 .1664 .0279 .0675 . 1064 .1443 .1808 .0319 .0714 .1103 .1480 .1844 .0359 .0753 .1141 .1517 .1879 .0080 .0478 .0871 .1255 .1628 .1985 .2324 .2642 .2939 .3212 .0160 .0557 .0948 .1331 . 1700 .2054 .2389 .2704 .2995 .3264 .0199 .0596 .0987 .1368 .1736 .2088 .2422 .2734 .3023 .3289 0.5 0.6 0.7 0.8 0.9 .1950 .2291 .2611 .2910 .3186 .2019 .2357 .2673 .2967 .3238 .2157 .2486 .2794 .3078 .3340 .0000 .0398 .0793 .1179 . 1554 .1915 .2257 .2580 .2881 .3159 .3413 .3643 .3849 .4032 .4192 .4332 .4452 .4554 .4641 .4713 .0239 .0636 .1026 .1406 .1772 .2123 .2454 .2764 .3051 .3315 .3554 .3770 .3962 .4131 .4279 .4406 .4515 .4608 .4686 .4750 .3438 .3665 .3869 4049 .4207 .3461 .3686 .3888 .4066 .4222 .3485 .3708 .3907 4082 .4236 .3508 .3729 .3925 .4099 .4251 .3531 .3749 .3944 .4115 .4265 .3577 .3790 .3980 .4147 4292 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 .4345 .4463 .4564 .4649 .4719 .4357 .4474 .4573 .4656 .4726 .4370 .4484 .4582 .4664 .4732 .4382 .4495 .4591 .4671 .4738 .2190 .2517 .2823 .3106 .3365 .3599 .3810 .3997 .4162 .4306 .4429 .4535 .4625 .4699 .4761 .4812 .4854 .4887 4913 .4934 .4951 4963 .4973 .4980 .4986 .4990 .4993 .4995 .4996 .4997 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 4.0 4.5 5.0 6.0 .2224 .2549 .2852 .3133 .3389 .3621 .3830 4015 .4177 .4319 .4441 4545 .4633 .4706 4767 .4817 .4857 .4890 .4916 .4936 .4952 .4964 .4974 .4981 .4986 .4990 .4993 .4995 .4997 4998 .4772 .4821 .4861 .4893 .4918 .4938 .4953 .4965 .4974 .4981 .4987 .4990 .4993 .4995 .4997 .4998 .49997 .499997 .4999997 .499999999 .4778 .4826 .4864 .4896 .4920 .4940 .4955 4966 .4975 .4982 .4987 .4991 .4993 .4995 .4997 .4783 4830 4868 4898 .4922 .4941 .4956 .4967 .4976 .4982 .4987 .4991 .4994 .4995 4997 .4394 .4505 .4599 .4678 .4744 .4798 .4842 .4878 .4906 4929 .4946 .4960 .4970 .4978 .4984 .4989 .4992 .4994 .4996 .4997 .4788 .4834 .4871 .4901 .4925 .4943 .4957 .4968 .4977 .4983 .4988 .4991 .4994 .4996 .4997 .4793 .4838 .4875 .4904 .4927 .4945 .4959 .4969 4977 4984 .4988 .4992 .4994 .4996 .4997 .4418 .4525 .4616 .4693 .4756 4808 .4850 .4884 .4911 .4932 .4949 .4962 .4972 .4979 4985 .4989 .4992 4995 .4996 .4997 .4803 .4846 4881 .4909 .4931 .4948 4961 .4971 .4979 .4985 .4989 .4992 4994 4996 .4997 768 Appendix
A B с X2 1 Y 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 X1 28 43 45 49 57 68 74 81 82 86 101 112 114 119 124 12.6 11.4 11.5 11.1 10.4 9.6 9.8 8.4 8.8 8.9 8.1 7.6 7.8 7.4 6.4 134 126 143 152 143 147 128 119 130 135 141 123 121 129 135