Please use the appropriate attached distribution table:

4. A researcher claims that at least 10% of all football helmets have manufacturing flaws that could potentially cause injury to the wearer. A sample of 200 helmets revealed that 16 helmets contained such defects. Use a-0.05. (a) Test the hypothesis that the defective rate is greater than 10% using the P-value b) Test the hypothesis using a conference interval on the defective rate. J-as zu 126 1. TABLE II Cumulative Standard Normal Distribution -4.00 08 -0.07 -0.14 -9.95 -0.04 -0.03 1 00 -19 0.00001 0.000034 0.0000% 0.000037 0.000019 0.00004 0.000022 0.000044 0600046 ODOODLE -318 0.00000 0.000052 0.000054 0.000057 0.000059 0.000062 0.000054 0.000067 0.00000 0.000072 -3.7 0.000075 0.000076 0.000022 0.000085 0.000088 0.000092 0.000096 0.000000 0.000104 0.000108 -3.6 0.000112 0.000117 0.000121 0.000126 0.00001 0.000136 0.000142 0.00097 0.000153 0.000159 -35 0.000165 0.000172 0.000179 0.000185 0.000193 0.000 0.0002 0.000216 0.0003 0.000033 -14 0.000242 0.00051 0.000280 0.0.000 0.000280 0.00001 0.000302 0.000313 0.000325 0.000337 -33 0.000350 0.00022 0.000376 0.000390 0.0004 0.000419 0.000134 0.000450 0.000467 0.000483 -32 0.000 0.00051 0.000538 0.000151 0.000 0.0001 0.00049 0.000641 000.000 -11 0000711 0.000736 0.000762 0.000 0.00016 0.000845 0.00064 0.000904 0.000 0.0009 -10 0.00 0.00105 0.001070 0001 0.001144 0.001183 0001223 0.001364 0.001306 0001350 -29 0.001395 0.001441 0.001489 0001538 0.001589 0.001641 0.001695 0.001750 0.001807 0.001366 -28 0.001926 0.00198 0.0006 0.00218 0.00016 0.002236 0.002327 0.0004 0.07 0.002555 -27 0.000635 0.002718 0.002503 0.0028 0.000980 0.009072 0.000367 0.003266 0.003 00467 -26 0.003573 0.00051 0.00379 0.003901 0.004005 0.004145 0.0022 0.00496 0.004527 0.004661 -2.5 0.004799 0.00090 0.005085 0.005234 0.005386 9008543 0.005703 0.005868 0.006097 0.00210 -2.4 0.006367 0.006568 0.006956 0.00097 0.007143 0.00754 0.0075 0.007750 0.007976 0.006198 -23 0.008424 0008656 0.008894 0.009137 0.009367 0.009642 0.0003 0010170 00 0.010724 -22 G11011 001130400116 0.011911 0.012234 0.012545 0.012814 0.013209 0.013553 0.019903 -2.1 0.054262 0.01429 0.015003 0.0156 0015778 0.096177 0.0165 0.017003 0.017429 0.017664 -2.0 0.016309 0.016763 0019226 0.01 0.020112 0.000675 0.001178 0.621692 0.022236 0.002750 -19 0023295 0.023852 000419 0.094918 0.005 0.036190 0.006803 0.00129 0.07067 0028917 -18 0.0097 0.0004 0.000742 003143 0.002157 0.003854 0.02 0.034379 0035148 0099990 -1.7 0.036727 000753 04 0.00201 09 0.000929 0.011815 0042716 0.003633 0.04545 -16 0.04554 0.646479 0.047460 0045457 0.09671 0.080808 0.005 0.083616 0.033.09 0051794 -1.5 0.055917 0.057053 0.058208 0.098380 0.060571 0.061780 0.063008 0.064356 0.065522 0.066807 -14 0.060112 0.000437 0.000751 0.072145 0.071529 0.07094 0.076359 007784 0.019270 6.080759 -13 0.082254 0.083793 0.38) OS CORSOK 0000123 0.091759 0.098418 0,095098 80 -12 0096525 0.10023 0.00042 0.108235 0.10566 0.107488 0.1095) 0111233 0113140 0115070 -1.1 0.117093 0.119000 0.121001 0.123034 0.125072 0.127143 0.129238 0.131357 0.133500 0.135666 -1.0 0.13787 0.1007 0.142310 0148572 6.146859 01491700.151505 0.153864 0.156848 0.158655 -09 0.161087 0.163543 0.16.003 0.168528 0.171066 0171009 0.176185 0178786 0.181411 0.134060 -08 0.186733 0.189490 0.192.50 0.194894 0.197662 0.200454 0.203209 0.206105 0.208970 0.211855 -07 0.214764 0.217696 0220650 0.223627 0.226627 0.229650 0.232695 0.235762 0.23852 0.341964 46 0345097 0.34252 0.21 0.254607 0.257845 0.367056 0.264347 0.267629 0.270931 0.27653 -05 0.27759 0.260957 0.286339 0.237740 0.291160 0.29459 0288056 0301532 0305026 0.308538 -04 0.312067 0315614 031917 0.327258 0.336355 0.329 0.333578 0.337243 0.3600) 0.344578 -0.3 0.4 0.351973 0.3386910_359424 0.363169 0_366928 0_320700 0.374434 0.378281 0.1.2009 -0.2 0.383.06 0.80799 0.393580 0977432 0401294 0.405165 0499046 0412936 041614 0420340 -0.1 0.434655 0.428576 0432505 0.4X5441 0440382 0.40 0.468283 0452342 0.456205 00172 0.0 0.454144 0.458119 0472097 0.476078 0.48061 0.484047 0467033 0492022 0.49600.500.000 TABLE - III Cunulative Standard Normal Distribution (Continued 0.0 0.500000 0.509989 0.507978 0.511957 0.519953 0519939 0532927 0.527903 0.531831 0.535855 01 0339628 007 0547758 0.551717035760 0.39618 0563559 0.567495 057144 0375345 02 0.579260 0.583166 0.587064 0.590954 6.594835 0.999706 0.002568 0.606420 0.610261 0614092 03 0617911 0.621719 0.125516 0699300 0633072068 0640676 0644309 0.648027 0.681782 0.4 0.685422 0.0 0.662757 0.666402 0.870031 0.673645 0.677242 0.680822 0.684386 0.687933 05 0.691462 0.694914 0.698458 0.70194 0.705401 0.7085400712310 0.71861 0.719043 0723405 0.6 0.725747 0.729019 0.792371 0.735653 0.738914 0.742154 0.145973 0.746571 0.751745 0.754903 0.7 0.758036 0:761145 0764238 0.767305 0.770350 0.773373 0776373 0779150 0.783305 0.785236 08 0788145 0.791000 0.7492 0.77 0.77546 0.002334 0.0106 0.80750 0330570 081326 09 0819940 0.816589 0.6021214 0823815 0.826391 0.828944 0.31472 0.833977 0.836457 0.838913 LO 0841345 0.843752 0.8461% 0.943495 0.850130 0.853141 0.855428 0.857090 059929 00143 1.1 0.864334 0.366500 0.368643 0.0762 0.872857 0.874928 0.876876 0.872999 0.81000 0.882977 1.2 0.854930 0.88680 0.588767 0.89651 0.892512 0.698350 0.896165 0.897956 0.999727 0901475 13 901199 0901202 e 090341 OSO? 0.911082 0915 6.914657 09162 091773 14 0012343 0.920730 0.922196 0.923641 0.9250366 0976471 0.927855 0.928219 0990563 0931588 15 0933199 0934478 093574 099920988220 0939429 0940620 0.9417920942047 0944063 16 094520046801 0.7384 09448449 094947 0.980529 0951543 0.9525400953321 0954486 1.1 0.955435 0956367 0.957284 0.958185 0.999071095994 095 0961636 0342 0943273 13 0.964090 0964852 2.921 0.966375 0.967116 0.967843 0.568357 0.901258 097946 0970621 1.9 0.971283 0.971953 0.972571 0.973197 0973810 0974412 0975002 0975581 0976148 0976705 20 0977250 0977784 097838 0978822 0979325 0979818 0.980301 0.980774 091237 0983691 21 0982136 0989571 0.952997 0.983414 0.93823 0.954222 0.994614 0.98497 0.985371 0.985738 22 0986097 0.995447 0.98791 0987126 0987455 0997776 0089 0989% 96 098989 23 0989275 0.999556 0989830 0990097 0.05 0.980613 0.10863 0.991106 0.991144 0.991576 24 0.99.60 0.922004 0.992340 0.992451 0.992656 0.992857 0993053 0993244 6.993431 0993613 25 0.993790 0.999% 0.994132 0994297 0.91457 0904614 -0.94366 0.90 0.500 0.9301 2.6 0.99839 099547 0.995606 0.965731 0.95835 0.995975 0.916093 0.996207 0.998319 0.996477 2.7 0.986833 0.996636 0.996736 0.99833 0994228 0.997000 97110 0997197 097282 9736 28 099745 0997523 0997999 097673 097744 0.9714 0.92 0.977945 0.9990120.998074 29 0914 0.99819 0.916250 0.998305 0.998059 0.995411 0.995462 0.998511 99859909905 3.0 0.995650 0.998094 0.9987% 0.998777 0978817 0995856 098193 0.998930 0.999%65 0.9999 3.1 0.02 0.99865 0.90 0.999126 0.999155 0.999184 0.99211 0.999238 0.9999354 0.99289 3.2 0.999313 0.999336 0.999399 0.999381 0.999402 0.999423 0999443 0999.52 0999681 0.999499 33 2999517 099953 0999550 6 0.9991581 0.99956 0.9%810 0.999624 0.974538 0.80 34 0.6 0.999615 096 0.9 0.99709 0.999720 0.999730 0.999740 949 99758 15 96 9776 974 0.92 0.977300 0.97730 S 0.99821 0.999128 097835 26 941 97 0.9 0.972 07 994 0.9787 0.1977 19 6999893 099 o O VOS 12 0.IS IS 0.977122.mas 96 0.999918 999940999943 0996 0.987915 0.974930 2.9 0.999933 09/0954 0.9993% 92288 0 0 BMS LICA B. W. so 3.84 10 1244 11.01 1283 16.01 17.53 15.09 14.75 1681 18.55 2024 2009 2196 23.39 15.51 2472 28-30 21.00 22.5 23.68 25.00 26.00 21.92 23:34 24.74 26.12 31.32 10:58 TABLE. IV Percentage Points of the Chi-Squared Distribution 995 990 975 .100 02 2.21 2 01 05 1.99 3 38 2:37 4 1.06 7.78 5 .55 115 1.61 4.35 9.24 6 2:20 535 10.05 7 124 2.17 12.00 134 2.18 2.73 249 7.34 9 1.73 2.09 2.70 4 10 2.16 2.55 3.25 994 15.99 4.57 3.54 10.94 17.25 12 3.00 3.37 6.30 18.55 13 3:57 5.01 3.29 7.04 14 6.57 7.79 15 7.26 22:31 16 5.14 5.81 6.91 7.96 9:31 15.4 23.54 17 5.70 756 10.09 16.34 34.77 16 7.01 1037 17.34 25.99 19 6.84 8.91 10.12 11.65 27-20 20 10.85 12:46 19:34 8.03 1028 11.99 13N 20.34 1098 1234 14.04 11.69 22.44 32.01 24 9.89 10:36 12.40 15.66 2334 25 10.32 11.52 1461 16,47 20.34 11.16 13.84 15:38 17.29 25.34 27 12.88 16.15 16.74 28 12.46 13.57 15:31 16,93 18.94 27.34 37.92 13.12 16.05 17.71 19.77 12.79 14.95 16.79 60 22.16 29.05 39.34 27.99 29.71 32.36 34.76 37.49 49.33 6.17 60 35.53 37.48 40.45 46.46 $9.39 14.40 70 51.74 35.33 69.33 85.53 51.17 57.15 6428 7933 90 99.20 69.13 73.29 89.33 100.57 100 07.30 20.06 28.85 30.19 31.53 34.27 3572 37.16 28.87 10.14 36.19 37.57 14.17 35.48 36.7% 49,00 41.40 33.92 35.17 16:42 45.56 40.65 41.92 38.19 40.11 45.61 45.95 44.46 5099 42.77 46.98 55.26 66.77 7142 76.15 79.49 91.95 95.02 004210432 101.88 106.63 112.33 116.32 113.14 124.12128.30 120.94 140.11 01 0.0025 63657 12732 9925 001 318,31 1 6.965 31.998 12.924 8.610 4 3.77 10.213 7.173 3.59 4.773 S 6 1.709 3.388 3.250 5.959 5.408 5.041 4.751 2.8% 2821 2.764 2718 2.681 2650 4497 4.00 3.990 3.425 3.372 3.326 3.787 3.733 TABLE V Percentage Points of the Distribution 40 28.10 45 135 1.000 3.078 2 .816 1.886 2920 3 .265 2.353 2011 2.132 2.776 1456 2015 2571 .715 1.440 1.90) 2447 2 26.3 .711 1415 1.895 8 1.397 9 260 .703 1.833 2.262 10 700 1.372 1.312 2.228 1997 1.796 2.201 1695 1.742 2.17 694 1.350 1.731 2.160 612 1.345 1.761 15 258 1.341 1.753 2.131 16 258 690 1.337 1.70 2.120 12 257 1.333 1.700 2.110 18 257 1.3 1.7 2.101 19 257 1.729 2.099 257 1.325 1.725 2.085 21 1.721 2.080 22 686 1.217 2014 23 1.319 1.214 24 256 1.31% 1711 25 256 1.316 1.708 26 256 1.315 1.706 2.056 256 1.314 2.052 130 1.701 2.048 2.045 30 1310 2012 1.303 2021 1.296 1671 2.000 120 1.289 674 1.960 4:07 4015 2.583 3.923 3.222 3.197 3.174 3.159 2352 2399 2528 2.518 3610 3.579 3055 2012 2971 2.947 2.921 2.898 2.678 2.851 2.45 2:31 2819 2.807 2.797 2.187 2.779 2.711 2.763 2.756 2.950 2.704 3.104 3.091 3.074 3.505 3.485 3.467 3.819 3.792 3.767 9.145 3.725 3.709 2.500 2.492 2.455 249 2.473 2.457 2.462 2.457 2.423 2.390 3.435 3.421 3674 3.057 3.047 3.038 3.030 2.971 2.915 17 3.551 154 3373 2.617 2.376 3.160 3.090 2.807 Sample 2 3 15.978 5.847 18.800 6919 0.99 242.300 160193 18930 9.398 22:401 4 3.919 4.152 3.723 3452 7.855 6.345 5 6 7 $ 9 10 10.260 101 7.187 $.337 4.613 4.147 2.24) 4936 3.125 3.018 2933 2535 246) 2.404 2355 2314 5966 5.996 S08 5029 3.250 2130 4.045 3.870 3.727 29445 Values of for Two-Sided Intervals Confidence Level 0.95 Probability Coverage 0.99 20.167 32019 32.64 8974 9.916 6.370 8.299 4.275 3.712 4.414 5.795 4.521 3.369 4.007 5.248 4278 2136 3752 1891 3532 3.379 2.737 4.277 2.655 3.142 257 3.618 2529 3.012 3.955 3.562 2.480 - 2954 3.514 2.437 2.000 3.471 2858 3.254 3.433 2.366 2819 3.702 2337 2784 2310 2.752 3.615 2.723 3.577 2.264 3.363 3292 2.24 2673 3.312 3.270 2.235 3.251 2 208 2.631 3.170 2.140 2.529 3.350 2.052 2.445 3.001 2379 2.955 1956 2.920 3,021 1.907 2272 2.872 2.958 2854 1874 2233 2.934 14 15 16 17 18 4.737 4.605 2.805 2.756 2.713 2.676 2.643 2614 2.568 2.564 2.543 2.246 2.219 2.194 3.500 3421 3.345 2.80 2.750 2.909 4230 3.221 2.168 4,100 21 22 23 24 25 2.152 2.135 2.018 2.100 2099 2077 2,025 1999 1.916 2.584 2.551 2.522 2474 3.078 3.040 3.004 2.972 2.841 2.677 2.576 3917 3.908 3.733 SIR 50 2385 2.247 2.167 2.103 2.060 2026 2334 2.284 2.245 2222 2.202 2.185 2.172 70 2.454 3.29% 3.225 2.173 90 100 1973 2355 0.99 0.95 17.370 TABLE.XII Factors for Tolerance intervals (Continued) Values of k for To Sided Intervals Confidence Level 0.90 0.95 Sample Probability of Coverage She 0.90 0.95 0.99 0.90 0.95 0.99 10.253 13.090 18.500 20.581 26.260 37.094 3 5.311 7.340 6.155 7.656 10.353 3.957 5.438 4.162 5.144 7.042 5 2.742 3.400 4,666 3.407 4.203 5.741 6 2.494 3.092 3.006 3.708 5.062 7 2.333 2.894 3.972 2.755 3.399 2219 2.754 3.783 3.187 4.354 2.133 2.650 3.641 2.454 3.031 4.143 10 2.066 2.568 3.532 2.355 2.911 3.981 2011 2.503 3.443 2.275 2815 3.852 12 1.966 2.448 3.371 2210 2.736 3.747 13 1.928 3.309 2.155 2671 3.699 14 1.895 2.363 3.257 2.109 2614 3.585 15 3.212 2.068 2.566 3.520 16 1.842 2.299 3.172 2.033 2.524 17 1.819 2.272 3.137 2.002 2.486 1.800 2.249 3.105 1.974 2453 3.370 1.782 2227 3.077 1.949 2.423 3.331 20 1.765 2028 3.052 1.926 2.196 3.295 21 1.750 2.190 3.028 1.905 2.371 22 1.737 2.174 3.007 1.886 2349 3.233 23 1.724 2.159 2.987 1.869 2328 1.712 2.145 2.9619 1.853 2.309 3.181 25 1.702 2.132 2.952 1.838 2292 3.158 1.657 2.000 2.834 1.77 2.220 3.064 1.598 2010 2.799 1.697 2.125 2.941 1.559 1.965 2.735 1.646 2.065 2.862 1.532 2694 1.609 2.022 2.807 1.511 2.662 1.581 1.990 2.765 80 1.495 1.890 2.638 1.399 1.964 2.733 90 1,481 1.874 2.618 1.542 1.944 2.706 100 1.470 1.861 2.601 1.527 1.927 2.684 0.90 103.029 13.995 7.380 5.362 4.411 3.859 3.497 3.240 3.048 2.898 2.777 2.677 2.393 2521 2.499 2.405 2.357 2.314 2.276 2.241 2.209 185.617 2.896 12.187 8.909 7.335 6,412 5.812 5.389 5.074 4.829 4633 4472 4337 4.222 4.123 4,037 3.960 3.891 3.832 3.777 3.727 3,681 3.640 3.601 3.447 6.578 5.406 4.728 4.285 3.972 3.735 3.556 3.410 3.290 3.189 3.102 3.028 2.963 2.905 2.854 2.808 2.766 2.729 2.694 2.662 2.633 2515 2.364 2.209 2.202 2.159 2.114 2.082 2.056 19 2.180 2.154 2.129 2.030 1.902 1.821 1.764 1.722 1.688 1.661 1.639 20 1.909 3.125 3.038 2974 2.924 2.883 2.850 wo R 1.596 5 6 7 8 9 10 + A Read aloud | Draw Highlight TABLE XI Factors for Constructing Variables Control Charts Factor for Control Limits X Chart VR Chart S Chart A. A d; D D. C. 3.760 1.880 1.128 0 3.267 0.7979 2 2.394 1.023 1.693 0 2.575 0.8862 3 1.880 729 2.059 0 2.282 0.9213 577 2.326 0 2.115 0.9400 s 1.410 483 2.534 0 2.004 0.9515 6 1.277 .419 2.704 .076 1.924 0.9594 7 1.175 373 2.847 .136 1.864 0.9650 8 1.094 337 2.970 .184 1.816 0.9693 9 1.028 308 3.078 .223 1.777 0.9727 10 973 285 3.173 .256 1.744 0.9754 11 925 266 3.258 284 1.716 0.9776 12 .884 249 3.336 .308 1.692 0.9794 13 848 235 3.407 .329 1.671 0.9810 14 .816 223 3.472 .348 1.652 0.9823 .788 212 3.532 .364 1.636 0.9835 16 .762 .203 3.588 .379 1.621 0.9845 17 .738 .194 3.640 .392 1.608 0.9854 18 .187 3.689 .404 1.596 0.9862 19 .697 .180 3.735 .414 1.586 0.9869 .679 .173 3.778 425 1.575 0.9876 21 .662 .167 3.819 .434 1.566 0.9882 22 .647 .162 3.858 .443 1.557 0.9887 23 .632 .157 3.895 .452 1.548 0.9892 24 .619 .153 3.931 .459 1.541 0.9896 25 12 13 14 15 16 17 18 15 19 .717 20 20 21 22 23 24 25