AP Statistics Problems #8

$36WDWLVWLFV7HVW,QIHUHQFHIRU2QHDQG7ZR:D\7DEOHVDQGIRU /HDVW6TXDUHV 3Dge 1 of 4 User Name: ___________________ Instructor: ____________________ Date:_________ (print clearly) Directions • • Neatly write your responses in the spaces provided. Use a blue or black pen. Don't write in the margins. Remember to complete the submission information on every page you turn in. Free Response: 2 questions, 52 points, 30 minutes 1. This table shows the number of defects, tallied by day of the week, in a manufacturing process: Number Monday 36 Tuesday 23 Wednesday 26 Thursday 25 Friday 40 The manufacturer is concerned that the number of defects is greater on Monday and Friday. Test, at the .05 level of significance, the claim that the proportion of defects is the same each day of the week. Be sure to include all steps of a hypothesis testing procedure. (26 points) ______________ © Copyright 2000-2009 Apex Learning, Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning, Inc. 2 Regression Analysis The regression equation is StopDist = Predictor Constant Coef –89. . All rights reserved.QIHUHQFHIRU2QHDQG7ZR:D\7DEOHVDQGIRU /HDVW6TXDUHV Page 2 of 4 User Name: ___________________ Instructor: ____________________ Date:_________ (print clearly) 2.75 57.50 78.0 Min Max 25.0 Q1 Q3 28. Inc.7053 0.86 28.$36WDWLVWLFV 7HVW. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning.36 88.47 R-sq = 98.00 44. Inc.000 R-sq(adj) = 98. The data in the following MINITAB output refer to an automobile's stopping distance (in feet) at different speeds.7 236.0 303.2% t-ratio –7. Data Display Row Speed StopDist 1 2 3 4 5 6 7 8 9 10 25 25 30 35 45 45 55 55 65 65 63 56 84 107 153 164 204 220 285 303 Descriptive Statistics Variable Speed StopDist Variable Speed StopDist N 10 10 Mean 44.0% ______________ © Copyright 2000-2009 Apex Learning. This material is intended for the exclusive use of registered users only.50 163.99 Stdev 12.68 Speed 5.10 p 0.5 160.00 65.00 56.9 Median TrMean 45.0 StDev 15.38 158.2707 s = 12.4 SEMean 4. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning. Test the hypothesis H 0 : β 1 = 0 and H a : β 1 ≠ 0. Inc. Inc. Find a 95% confidence interval for the slope of the regression line.QIHUHQFHIRU2QHDQG7ZR:D\7DEOHVDQGIRU /HDVW6TXDUHV Page 3 of 4 User Name: ___________________ Instructor: ____________________ Date:_________ (print clearly) A. This material is intended for the exclusive _____________ use of registered users only. (4 points) D. (7 points) ______________ © Copyright 2000-2009 Apex Learning. (4 points) C.$36WDWLVWLFV 7HVW. All rights reserved. Interpret the slope of the regression line. What's the equation of the regression line you'd use to predict stopping distance based on speed? (4 points) B. . $36WDWLVWLFV 7HVW.QIHUHQFHIRU2QHDQG7ZR:D\7DEOHVDQGIRU /HDVW6TXDUHV Page 4 of 4 (6XSSRVHLQVWHDGRIWHVWLQJH  β  \RXGHFLGHGWRWHVWH  β DJDLQVW Ha⠏:KDW3YDOXHZRXOGEHDVVRFLDWHGZLWKWKLVWHVW"SRLQWV. All rights reserved. ______________ © Copyright 2000-2009 Apex Learning. Inc. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning. Inc. . 0262 .0256 .0007 . rights reserved.3121 .0643 .1112 .0037 .0314 .1894 .1190 .0375 .0024 .3156 .4443 .0064 .2877 .0018 .4247 .05 .0344 .0559 .0202 .1562 .0170 .0869 .0465 .0485 .0721 .3050 .0016 .0026 .0008 .4404 .3745 .0006 .0212 .0022 .0034 .0005 .0192 .3897 .03 .0158 .1020 .0049 .1635 .4960 .0409 .0002 .2709 .0119 .0183 .3557 .0004 .0015 .0087 .1038 .0116 .0009 .0367 .0455 .0011 .1056 .1093 .6 -0.0179 .1292 .0392 .0003 .2266 .08 .4207 .8 -2.2578 .permission or redistribution prohibited.0244 .0080 .0004 .0041 .09 .0029 .1762 .0005 .2 -0.0002 .9 -2.1 -3.0708 .0051 .2090 .3446 .0023 .9 -0.0054 .0228 .0026 .1230 .2420 .4761 .1711 .0778 .0033 .4 -3.4 -1.3409 .0548 .0427 .1003 .4522 .2643 .3015 . Advanced registered © Copyright Copyright 1999 1999-2009 Apex Learning.2 -2.3632 .0122 .2981 .1251 .0031 .2033 .0084 .0023 .0951 .1685 .1922 .4641 ___________________ ______________ © APEX Online Learning.0003 .0003 .2 -1.9 -1.0020 .4 -0.0537 .0239 .0043 .0003 . without the express written of ApexisLearning.0048 .0207 .0934 .2 -3.0668 .0025 .0885 .0307 .0301 .1401 .0004 .0047 .0002 .0002 .0082 .0 -1.7 -1.0808 .0060 .3483 .0003 .0008 .3974 .0007 .8 -0.0014 .3821 .4801 .6 -1.0006 .1515 . Inc.0749 .0089 .3192 .0021 .0011 .1210 .0078 .0495 .3 -3.1314 .3783 .0069 .1446 .2743 .0044 .Inc.0793 .0019 .3 -2.1867 .0059 .2810 .0233 .0985 .2514 .0150 . .2119 .1949 .2912 .0901 . No portion of theseismaterials be exclusive reproduced in any form Any unauthorized copying.1611 .2611 .3707 .2451 .7 -0.0162 .1335 .0003 .1788 .0002 .0016 .2483 .3520 .1075 .0027 .0329 .0336 .0003 .0002 .0019 .0655 .0002 .6 -2.0006 .0125 . use of registered only.0143 .2236 .0618 .0359 .0012 .0188 .0 .2327 .0418 .0113 .0004 .0268 .3936 .1271 .0036 .2148 .01 .0322 .2676 .7 -2.0035 .0401 .0384 .0475 .0009 .0040 .4090 .2177 .2776 .1587 .4840 .0013 .07 ------------------------------------------------------------------------------.0018 .1539 .0217 .2546 .AP Statistics – Tables and Formulas Table: Standard normal probabilities z -3.0853 .4052 .0068 .3594 .0073 .3336 .0030 .3669 .0436 .0139 .0222 .0021 .0013 .1379 .0526 .1 -1.1131 .0032 . This material Placement is intendedand for AP theare exclusive trademarks of theusers College Board.3 -0.0003 .0099 .5 -3.0132 .0606 .3300 .AllAll rights reserved.0052 .0007 .0008 .0062 .3859 .0002 .4721 .0735 .2296 .0146 .0918 .0017 .0003 .4129 .0075 .02 .1151 .4168 .0838 .0505 .0571 .0013 .0250 .2061 .0102 .0281 .0006 .8 -1.0096 . This material intended may for the useorofredistributed APEX-enrolled students.04 .4013 .0694 .0002 .0005 .0010 .2946 .0107 .0294 .0011 .1 -2.2389 .4325 .0004 .0104 .0015 . reuse.3228 .0010 .0091 .1423 . Inc.1469 .0274 .0630 .0012 .1357 .0129 .4286 .0006 .5000 .0005 .0007 .0166 .3 -1.4483 .4 -2.2206 .0008 .0 -0.0045 .0823 .0038 .0010 .3372 .2005 .0197 .0446 .0516 .4602 .1977 .3264 .0764 .2358 .0009 .0351 .0005 .0968 .1841 .5 -2.0014 .1170 .0 -2.0681 .4681 .4562 .5 -0.0071 .0136 .0002 .0287 .1660 .5 -1.0055 .0066 .0005 .1736 .0094 .4364 .1 -0.0594 .3085 .1492 .0039 .4880 .0057 .0110 .1814 .0028 .0582 .0002 .0003 .4920 .0174 .0154 .00 .06 .0004 .2843 . 6808 .9251 . .1 2.6 2.6591 .9582 .6255 .7 0.01 .9991 .6844 .9706 .7 2.5793 .9998 .8365 .9 2.8944 .6736 .0 3.9968 .9984 .9793 .8413 .5 .9998 .9332 .7967 .6772 .8 1.9192 . Inc.8869 .9974 .8508 . reuse.7019 . unauthorized copying.9744 .02 .9441 .08 .8133 .9345 .9995 .4 0.7257 .4 3.8577 .9957 .9986 .9996 .8770 .7995 .9995 .5160 .6664 .3 0.9946 .9953 .8315 .9985 .9625 . This material Placement is intendedand for AP theare exclusive © APEX Online Learning.9484 .9066 .8238 .9015 .7611 .9916 .9599 .9115 .9963 .6406 .6368 .9474 .9719 .8186 .9987 .9990 .9082 .9633 .8340 .6217 .9545 .7 1.8708 .9980 .8888 .9803 .9997 .0 2.9131 .9495 .9616 .7794 .9909 .9979 .9987 .9890 .9207 .2 1.9846 .6 0.9956 .6628 .9998 ______________ ___________________ © Copyright Copyright 1999 1999-2009 Apex Learning.9997 .6141 .4 1.7704 .9995 .7939 .9964 .6517 .9699 .8997 .9864 .7190 .6 1.9357 .8485 .5596 .06 .9994 .5478 .9951 .6950 .9997 .Inc.9868 .5279 .8106 .9732 .9177 .9505 .9826 .9767 .9952 .9996 .9236 .9918 .9989 .9969 .9 1.9997 .5517 .9515 .9147 .8264 .7088 .9573 .4 2.9941 .9906 .9265 .5987 .8078 .9222 .9783 .9998 .9996 .5319 .9798 .6443 .9977 .6554 .9925 .9292 .9998 .9452 .9842 .8599 . rights reserved.9979 .9970 .9986 .9893 .9981 .7580 .8 2.9994 .9993 .8686 .5 2.5359 .9993 .9861 .9778 .05 .9996 .7054 .5398 .9992 .9974 .8212 .9978 .6480 .9934 .9463 .8643 . This material is intended for the exclusive use of APEX-enrolled any students.9961 .9972 .9960 .09 .AP Statistics – Tables and Formulas Table: Standard normal probabilities (continued) z 0.9649 .1 3.7324 .9162 .8749 .3 1. Inc.5040 .5871 .9940 .9761 .AllAll rights reserved.9875 .9394 .9943 .9998 .0 1.5239 .7823 .8790 .9834 .5080 .9996 .5948 .9726 .6985 .5 1.9850 .2 2.9994 .9997 .6026 .9985 .9656 .5910 .9994 .permission or redistribution prohibited. No portion of these materials may be reproduced or redistributed in form Any trademarks of the College Board.9976 .9418 .8621 .9982 .5438 .9977 .9641 .9854 .9966 .9997 .8925 .9554 .0 0.7157 .9608 .9983 .9922 .9936 .9971 .3 3.8438 .9 3.9959 .9998 .9713 .9965 .9756 .9319 .9306 .5675 .9967 .9927 .9896 .9788 .9099 .9955 .5120 .9564 .8531 .9382 .9878 .8 0.5000 .9995 .9998 .9738 .5832 .9991 .1 1. Advanced registered use of registered users only.9693 .9990 .9279 .9995 .9982 .9945 .7389 .6915 .9032 .9591 .7123 .9920 .9993 .2 0.9990 .8980 .8023 .9929 .9664 .7486 .9772 .9992 .8554 .9817 .9991 .9949 .6700 .5714 .9981 .6179 .7910 .1 0.9994 .7422 .9997 .9871 .5753 .9997 .9808 .9998 .9997 .9678 .9989 .8849 .9821 .8289 .9898 .9992 .7357 .9992 .7881 .7517 .9973 .5636 .9857 .8810 .2 3.9838 .5199 .5557 .9830 .6103 .9913 .3 2.6331 .9686 .9812 .9904 .9750 .00 .9884 .7549 .8665 .9975 .03 .7764 .8962 .07 ------------------------------------------------------------------------------.9901 .9987 .9984 .9962 .9996 .9911 .7224 .6879 .9988 .9993 .8830 .7673 .9998 .8159 .9998 .7734 .9988 .7852 .9881 .9887 .9931 .9429 .9997 .8729 .7454 .9671 .9049 . without the express written of ApexisLearning.9932 .9948 .5 0.9995 .8907 .8051 .9370 .7291 .6293 .9525 .9535 .7642 .8461 .04 .9938 .9406 .6064 .9989 .8389 . 703 1.326 98% .921 2.977 2.856 .047 1.675 .697 .676 1.02 15.056 2.055 3.250 1.005 63.718 2.684 .060 1.771 1.883 .796 1.398 2.861 .315 1.476 1.700 .079 1.350 1.764 2.711 .000 .896 2.048 2.119 3.408 5.093 1.032 3.851 .050 1.703 .858 .043 1.674 3.356 1.064 2.879 .365 3.299 1.681 .303 3.408 3.533 1.353 2.015 1.080 2.848 .898 2.638 1.741 .889 .099 2.701 1.990 1.862 .009 2.303 2.428 3.797 2.505 3.296 1.189 2.450 3.282 2.282 80% .833 1.355 3.056 2. Inc.567 2.307 3.318 1.690 .684 1.290 1.9% Confidence level C ___________________ ______________ © APEX Online Learning.943 1.067 1.855 .372 1.699 1.074 2.297 4.447 2.920 2.069 1.190 1.AP Statistics – Tables and Formulas Probability p t* t distribution critical values Tail probability p df 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 26 27 28 29 30 40 50 60 80 100 1000 ∞ .782 1.376 1.729 1.82 6.055 1.717 1.646 3.174 3.0005 636.781 4.145 2.150 2.819 2.721 1.365 2.792 3.101 2.841 4.92 8.109 2.873 .6 31.773 4.639 2.01 31.330 2.895 1. rights reserved.025 3.718 .678 .169 3.088 1.208 4.440 1.317 4.291 99.508 2.249 2.920 .3 14.328 2.479 2. This material Placement is intendedand for AP theare exclusive trademarks of theusers College Board.856 .383 1.314 2.866 .645 90% .674 50% .162 2.587 4.571 2.687 .306 2.221 4.058 1.646 1.688 .740 1.183 2.086 2.71 4.915 2.692 .078 1.787 3.177 2.058 1.684 .064 1.473 2.421 3.518 2.462 2.8% .697 1.604 4.104 3.173 5. reuse.768 3.679 .965 3.602 2.626 2.052 2.984 1.612 2. without the express written of ApexisLearning.959 5.485 2.845 2.579 3.100 1.396 3.813 2.598 4.323 1.858 .10 3.222 3.528 2.499 3.678 2.876 .282 1.147 2.264 2.679 .690 3.576 99% . Inc.869 5.850 3.845 .0025 127.865 .925 5.453 5.437 4.135 3.685 .878 2.397 1.686 .364 2.496 3.761 1.517 2.071 1.690 3.143 2.757 2.144 4.20 1.841 60% .467 3.261 3.552 2.037 1.073 4.711 1.753 1.746 1.937 2.859 .583 2.000 1.819 3.313 1.776 2.664 1.321 1.812 1.091 99. Advanced registered © Copyright Copyright 1999 1999-2009 Apex Learning.326 3.750 2.098 3.646 3.083 1.252 3.821 2.345 1.999 2.842 .074 1.745 3.978 .779 2.228 2.059 1.727 .423 2.179 2.3 22.Inc.685 .887 2.831 2.069 2.311 1.706 .054 96% .930 3.733 3.922 3.214 2.833 3.15 1.012 2.807 2.906 .896 .33 10.684 .960 95% .689 .300 3.581 2.683 .849 .047 3.140 4.314 1.029 3.172 2.747 3.671 1.091 3.154 2.066 1.552 3.870 .482 2.374 2.319 1.683 .235 2.449 2.60 12.677 .871 2.868 .492 2.611 3.686 3.962 1.551 3.030 2. This material intended may for the useorofredistributed APEX-enrolled students.21 7.816 .153 3.232 3.106 3. No portion of theseismaterials be exclusive reproduced in any form Any unauthorized copying.763 2.132 2.707 3.134 1.015 3.174 3.310 1. use of registered only.123 2.849 3.197 3.056 1.725 3.088 2.076 1.372 3.386 1.078 3.854 .325 1.038 3.66 9.110 2.341 1.485 3.5% .292 1.704 2.541 3.158 2.787 2.286 3.765 .333 1.714 1.659 3.756 2. .063 1.042 1.691 .108 1.197 2.330 1.067 3.363 1.250 3.081 2.694 .001 318.883 3.435 3.734 1.182 2.708 1.385 3.681 2.328 1.337 1.AllAll rights reserved.021 2.224 2.688 .205 2.042 2.055 1.807 99.971 2.359 2.660 2.610 6.057 3.045 1.725 1.785 4.460 3.706 1.89 4.119 1.156 1.201 2.500 2.25 1.886 1.497 3.467 2.195 3.695 .036 70% .860 .860 1.581 3.permission or redistribution prohibited.947 2.390 2.457 2.855 .403 2.061 .041 4.025 12.683 .650 2.416 3.998 2.624 2.05 6.09 7.857 .539 2.941 .686 .501 4.965 4.846 .771 2.316 1.893 5.167 2.060 2.303 1.131 2.660 1.061 1.057 1.963 1.318 4.707 3.262 2.045 2.861 2.120 2.093 2.160 2.415 1.390 3.863 .527 3.852 3.854 . )RUPXODHIRU%DVLF'HVFULSWLYH6WDWLVWLFV [ = ∑[ L   Q  Q − V[ = ∑ [ L − [ .$36WDWLVWLFV±7DEOHVDQG)RUPXODV )RUPXODV <RXPD\UHIHUWRWKHVHGXULQJWKHtest.  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