QUESTION 4 A machine that produces ball bearings reports that the average diameter is not 0.5 cm. A sample of 10 ball bearings was measured and it was found that the average diameter is 0.48 cm, and the population standard deviation is 0.05 cm. (a = 0.05) a) State the null hypothesis and the alternate hypothesis. (2 Marks) b) Find the critical values. (1 Mark) c) Calculate the test statistic (2 Marks) d) State your decision regarding the null hypothesis (1 Mark) e) Summarize the results. (1 Mark) If the average diameter is less than 0.5 cm and a = 0.01, what is the hypothesis and the critical values (3 Marks) [Total: 10 Marks) AREAS UNDER THE STANDARD NORMAL CURVE Bangler: 22196, then 04790 of the areas between 0 and 156 0196 12 2 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0595 0.0638 0.0675 0.0714 00753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0,1141 0.3 0.1179 0.1217 0.1255 0.1293 01331 0.136B 0.1406 0.1443 0.1480 0.1617 04 0.1554 0.1691 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1986 0.2019 0.2054 0.2088 0.2123 0.2157 02190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.7549 07 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0 2764 0.2794 0.2823 0.7862 0.8 0.2881 0.2910 02939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3166 0.3212 0.3238 0.3264 0.3289 03315 0.3340 0.3365 0.3389 10 0.3413 0.3438 0.3451 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3656 0.3709 0.3729 0.3749 0.3770 0.3790 0.3810 0.3630 0.3849 0.3869 0.3858 0.3907 0.3926 0.3944 0.3962 0.3980 0.3997 0.0015 1.3 0.4032 0.4049 0.4056 0.4082 0.4099 0.4115 04131 04147 0.4162 04177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 04279 0.4292 0.4308 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0,4418 0.429 0.4441 1.5 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 17 0.4554 0.4554 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 04699 0.4706 19 0.4713 04719 0.4726 0.4732 04738 0.4744 0.4750 0.4756 0.4761 0.4767 20 04772 0.4778 0.4753 0.4788 0.4793 0.4798 0.4803 0.4803 0.4812 0.4817 21 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4848 0.4850 0.4854 0.4857 22 0.4861 0.4864 04868 04871 0.4875 0.4878 0.4831 0.4684 0.4887 0.4890 23 0.4893 0.4896 0.4898 04901 0.4904 0.4906 0.4909 04911 0.4913 04916 24 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 04945 0.4946 0.4948 0.4949 0.4951 04952 26 0.4953 0.4965 0.4956 0.4957 04959 0.4960 0.4951 0.4962 0.4963 04964 27 0.4965 0,4966 0.4967 04968 0.4969 0.4970 0.4971 04972 0.4973 0.4974 28 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4962 0.4982 0.4983 0.4984 0.4984 0.4965 0.4985 0.4986 0.4985 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 NO N ON NEGATIVE Z Scores J Standard Normal (2) Distribution: Cumulative Area from the LEFT 2000 A2 4 5 6 7 08 09 -1.50 lower DO01 1000 1000 1000 0003 0005 100C - 1000 5000 2000 DOOS 0004 0006 0002 0005 0005 1000 9000 9000 6000 - 0009 0003 0004 0008 0000 com co 0010 DO13 0019 6000 2000 0100 1100 001 002 8000 100 SOO ROO 400 0004 0004 000 DOOS 2007 0010 2014 001 0020 0020 00 0037 DOS. 0049 0014 0018 0035 0034 9200 6100 00N OOK OBS 0047 0023 0032 0043 OOC 6200 0008 1100 5100 0900 1500 2900 2800 0075 000 0052 0061 001 9900 1 1900 0025 0036 0048 0064 DOBA 0110 DIO 6800 0003 0005 .0004 0004 0006 0008 0008 0012 Doe 00% 0096 0023 0022 COM 004 0040 COSS 0054 0073 oon 0096 0054 02 0M2 008 0207 2002 0262 0956 0123 0822 DO 0505 . 068 0605 0949 0885 3075 6710 COM OS SZIO 0080 0804 0136 004 0222 0281 ORSI 0129 0166 0212 ONIO 0099 0079 0102 002 0170 0217 0974 0344 0427 0525 0543 0778 IMO 0087 013 0145 088 0239 0179 0228 0287 0359 0446 0548 M2 0154 097 02:50 034 2920 399999999999999999999 1050 006 DI 0233 0294 0367 0455 0559 CONC DERO ABS 0384 US 0582 0708 870 PESO DROB 0969 SEO ONA ESHO 8375 0465 0571 0694 08.30 2003 190 01 SCHO 0723 0869 1030 230 IS 0356 och 0516 0630 ONA 0918 1093 1292 1955 1752 2033 2137 2543 0905 US 9504 ISOT 3020 1910 2587 OLE IT 0537 0655 0793 0951 JU 3335 3562 1814 2090 259 2709 3050 3409 3783 AGB 4562 m2 1514 3539 7 200 2350 2676 29 190 SPX 1841 229 2420 2743 ONK SEX 971 2265 394 2148 2878 MISE 1922 2206 25 2843 3192 2483 ISHT 3085 492 3736 2005 2296 2011 2946 3900 3569 4052 40 4340 sor OLET 949 2235 2546 2877 1228 1994 2014 4354 1264 3632 3446 3821 4207 4502 5000 ESSE 3372 JOS 4129 4522 1920 3336 1707 4090 4483 1880 2776 3121 3483 1859 DOY 3:56 3520 3897 4286 4681 3936 4125 AZZI 4404 40 430 19 Y 4641 NOTE: For values of below-343. use 0.0001 for the area. Uwe these common values that result from interpolation: SCORE A -1645 0.0500 -2.575 0.00504 POSITIVE z Scores (continued) Cumulative Area from the LEFT 0 0 0 0 0 0 0 0 00 5000 3080 ONS SICS 0165 CW 5636 6026 GADG 6722 7123 2054 7764 ROC 3054 SL seeeeeeeee 251 SC IBC SMC IK SON RO 190 OSA HET 836 2554 LIST DYW GNS OUZE 6900 h 1105 DIOS GEOG 115 CM TE 2015 2515 1992 90 3279 3406 955 9608 66 5279 5370 5350 SES 5714 5753 5064 SIOS 04 5443 5480 557 5000 1844 5029 7190 724 26 2545 J714 2018 3706 833 1365 35 21 370 350 880 2900 1997 3015 912 901 9292 9306 Se 5429 9925 3535 9545 016 9125 SES 909 5706 3751 986 9707 SSON S012 50 9050 9054 3857 3864 SE? 300 31 9903 9945 9912 954 99.995 9992 9952910 972 937594 999 9900 9985 9306386 105 1655 1656 INS W OSES 9040 500 5099 5308 5438 508 55U 5557 55% 5795 5812 5871 5948 5987 619 1217 5255 5291 630 04 6554 6591 6700 5736 8915 6950 7088 7257 724 7334 7151 7329 7422 .7580 7611 242 2073 7204 J734 7910 1939 7995 1021 1550 3986 230 3209 8413 8436 16 3485 8908 2531 U M 2565 8686 NOU 3729 12 1849 BABE aso 8925 1944 9049 9066 14 9992 5207 9236 925 9265 15 9545 5357 3590 3382 3M 16 9463 9484 3095.3505 9554 9564 9573 9582 954 9543 9656 9664 967 978 19 SU 9719 90726 9782 9744 20 9772 574 9783 9788 9790 23 9821 9530 SEM 9008 so 22 9861 9M4 9040 9871 S873 90 23 5895 9896 Se 901 9904 24 9920 122 9925 9927 25 390 9940 94 9943 9345 25 9956 9952 9950 .1960 9965 9966 OG S969 9370 22 9974 9925 9976 9977 9978 29 .9982 9923 9984 9384 SH 9387 9960 9908 9989 11 99% 9991 9961 9992 32 9995 9194 9994 9994 9994 995 9995 096 996 2007 9997 9997 9997 9997 3.50 9999 and up NOTE: For values of rabow 145, 120.9999 for the area. "Use these common values that result from interpolation 200 A 1645 0.9500 2.975 09950 MOS 1605 9026 9803 9646 SARI 6006 1066 6286 3166 9931 2006 914 ISOS 5966 1766 30 9971 9879 9985 LIS CAGE 165 1866 GT 9987 6066 OME 2666 man 0665 1866 9992 .9954 0056 1666 5566 9666 9093 9995 5666 9646 1605 665 9995 99% 3997 2016 2566 9979990 Connelles Carline Oil Level 0901645 10 0.99 255 550 STUDENT'S DISTRIBUTION 30% 95% 99.9% 0.100 0.0005 Confidence interals,c 90% 98% 998 Level of Significance for One-Tailed Test, a 0.050 0.025 0.010 0.006 Level of Significance for Two-Talled Testa 0.10 0.06 0.02 0.01 6.314 12.705 31.821 63.657 2.920 4.303 6.965 9.925 2353 3.162 4.541 $341 2.132 2776 3747 4604 2015 2571 3.365 4.032 0.20 1 2 3 4 5 3.078 1.886 1.638 1533 1.476 0.001 136.619 31.599 12924 8.610 6.869 1.913 1.095 6 7 8 9 10 1440 1415 1.397 1.383 1.372 1.860 1.833 1.812 2447 2355 2.308 2262 2.228 3.16 2.990 2.896 2.821 2.764 3.707 3.499 3.355 3.250 3.169 5.959 5.408 5.041 1.781 4587 1360 11 12 13 14 15 1.356 1.350 1345 1.341 1.796 1.782 1.771 1.761 1.753 2201 2.179 2.160 2.145 2.131 2.710 2681 2650 2.624 2.502 3.108 3.055 3.012 2977 2917 4437 4318 1.221 4140 4.073 16 17 18 19 20 1.337 1.333 1.330 1328 1.325 1.746 1740 1.734 1729 1.725 2.120 2.110 2 101 2093 2006 2583 2567 2.552 2539 2.528 2.921 2.898 2878 2.851 2845 4015 3.965 3.922 3.363 3.850 22 1.323 1.321 1.319 1.318 1.316 1.721 1.717 1714 1711 1.700 2080 2.074 2.069 2.064 2060 2.518 2.500 2.500 2492 2485 2831 2819 2.807 2.797 2.787 3.819 3.792 3.768 3.745 3.725 24 25 * &SS 88 233 26 27 28 29 30 1.315 1314 1.313 1.311 1.310 1.708 1.703 1.701 1.699 1.697 2056 2052 2048 2045 2012 2.479 2.473 2.467 2462 2457 2779 2771 2763 2756 2.750 3.707 3.690 3.674 3.559 3.546 2021 40 60 120 1.303 1296 1289 1282 1684 1.671 1.650 1.645 2423 2390 2.358 2.326 2.704 2660 2617 2.576 3551 3.460 3.373 3.291 1980 1.990 Degrees of Freedom to the Denmater # mmmm 12 w %m s # mm m wwwmmmmm mmmmmmmmmmm mmmmmmm % mm%%% N Degustare 18:15 X X SIGNIFICANCE,
