Reference:

Cumulative area to the left of negative z scores 11/8/22, 12:56 AM NEGATIVE z Scores 0 Standard Normal (z) Distribution: Cumulative Area from the LEFT 06 07 .08 .09 .04 .05 -3.50 and .00 .01 .02 .03 lower .0002 -3.4 -3.50 and .000 .0003 lower .0001 0003 .000 .0003 000 -3.3 000'S .0003 .0003 .0004 .0004 .0003 -3.4 0004 0004 -3.2 0005 0005 .0004 .0004 0005 0005 0006 .0006 0006 .0006 0005 -3.3 0005 2007 0007 -3.1 0006 0007 0007 0008 -3.2 1009 DOO 0008 0008 0010 -3.0 0010 -3.1 0010 0011 .0011 0012 0011 0012 .0014 -2.9 0013 0013 .0013 .0016 0015 0015 0014 -3.0 .0017 0016 -2.8 0018 0020 0019 0018 .0021 .0021 -2.9 0019 0023 0022 .0026 -2.7 1025 10124 1027 0026 .0030 .0029 -2.8 0031 .0033 0032 0038 0037 0036 -2.6 0035 0034 -2.7 0040 0039 004 0041 0049 0048 -2.5 0052 1051 -2.6 0047 0045 0044 005 0055 0054 .0064 -2.4 0068 0062 1060 1059 0068 0078 0075 0073 0071 .0069 -2.5 0087 0084 -2.3 0080 -2.4 009 0091 0089 0082 0099 -2.2 0102 0096 0116 0113 0110 0104 0119 -2.3 0107 0122 0132 0129 0125 0146 0143 -2.1 0136 .0154 0150 -2.2 0139 0166 0162 0158 0170 0188 0183 -2.0 0174 0192 -2.1 0179 0202 197 0212 0207 0233 -1.9 0222 0217 0256 0250 0244 0239 -2.0 0228 0268 0262 0294 -1.8 1281 274 0287 .0322 0314 030 0301 -1.9 033 0329 0367 -1.7 0351 0344 0392 0384 0375 -1.8 0359 0401 0427 0418 0409 0455 -1.6 0446 1436 .0495 0485 0475 0465 -1.7 0526 0516 0505 0582 0571 .0559 -1.5 -1.6 0548 0537 0618 .0606 0594 1643 0630 0694 0681 -1.4 0668 0655 .0721 0708 -1.5 0764 .0749 0735 -1.3 0778 0853 1838 0823 -1.4 0808 0793 0885 0869 1934 0918 0901 0985 -1.2 0951 .1038 102 1003 -1.3 1968 109 1075 .1056 1190 1170 -1.1 1151 1131 111 1210 -1.2 1271 1251 1230 -1.0 1335 1314 1292 1401 .1379 -1.1 .1357 1469 1446 1423 1492 1611 -0.9 1562 1539 ,1515 .1685 166 1635 -1.0 1587 ,1711 1788 176 173 1867 -0.8 1841 1814 1922 1894 -0.9 2005 .1977 1949 -0.7 2090 2061 2033 2177 2148 2119 2266 2236 2206 -0.8 2296 2451 -0.6 2420 2389 2358 232 2483 2546 2514 -0.7 2643 2611 2578 -0.5 2709 2676 .2810 2776 2877 2843 -0.6 2743 3015 298 2946 2912 3050 3156 .3121 -0.4 -0.5 3085 3300 3264 3228 3192 3372 3336 3520 3483 -0.3 3446 3409 -0.4 3669 3632 3594 3557 3859 -0.2 3783 3745 3707 3936 3897 -0.3 3821 4090 4052 4013 .3974 4247 -0.1 4207 4168 4129 4325 4443 4404 4364 4286 -0.2 4641 1562 4522 4483 -0.0 -0.1 4602 4840 4801 4761 4721 4681 4880 5000 4960 1920 60 05 .OZ 08 -O.C 03 04 .06 00 01 02 NOTE: For values of z below -3.49, use 0.0001 for the area. 1/2 https://mylab.pearson.com/Student/PlayerHomework.aspx?homeworkld=627 170671&questionId=1&flushed=false&cld=6988267¢erwin=yes Cumulative area to the left of negative z scores 11/8/22, 12:56 AM "Use these common values that result from interpolation: z Score Area -1.645 0.0500 -2.575 0.0050 2/2 https://mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=627 170671&questionId=1&flushed=false&cld=6988267¢erwin=yesCumulative area to the left of positive z scores 11/8/22, 12:56 AM POSITIVE z Scores 0 Cumulative Area from the LEFT -08 .09 .06 -07 0.0 .02 .03 .04 -05 .5239 .5279 .5319 5359 .00 .01 5160 .5199 5753 0.1 5080 5120 5714 5040 5636 .5675 0.0 5000 .5596 .5517 5557 6141 0.2 5478 606 610 0.1 5398 5438 5948 5987 6026 0.3 5910 6480 6517 5793 5832 5871 6368 6406 6443 0.2 6331 3879 0.4 6255 6293 6772 5808 6844 03 6179 6217 6664 6700 6736 0.5 7157 7190 7224 6554 3591 5628 7088 7123 0.4 6985 7019 7054 7549 0.6 7454 748 7517 6915 5950 05 7357 7389 7422 7823 7852 0.7 7324 7794 7257 7291 7764 0.6 .7704 7734 8133 0.8 7642 .7673 810 8051 8078 0.7 7580 7611 .8023 0.9 7967 .7995 8389 7910 7939 .8315 834 8365 0.8 7881 .8264 8289 1.0 8212 8238 3554 3577 8599 8621 8159 8186 8485 .8508 8531 1.1 8461 8810 8830 8790 1.0 .8413 3438 8770 8729 8749 8997 9015 1.2 8686 8708 8962 898 1.1 8643 8665 8944 8907 892 1.3 3869 8888 9147 9162 9177 1.2 8849 9082 9099 9115 9131 9319 1.4 9066 9251 9265 9279 9292 9306 1.3 9032 9049 9441 1.5 9222 9236 9429 9192 9207 9394 9406 941 1.4 9545 1.6 9370 9382 9535 1.5 .933 9345 9357 9505 9515 9525 9495 9633 1.7 9484 625 9463 9474 9608 9616 1.6 9452 9599 1.8 9573 9582 9591 2699 970 9554 9564 0693 1.7 9671 9678 3686 2664 1.9 3656 .9756 9761 .9767 9641 2649 .9750 1.8 .9738 9744 9812 9817 9726 9732 2.0 9808 1.9 9713 9719 9798 9803 9857 2.1 9778 9783 9788 9793 9854 2.0 .9772 983 .9842 9846 9850 983 9887 9890 2.2 9830 21 9821 3826 .9878 9881 9884 9875 9916 2.3 3864 9868 9871 9913 9861 9909 9911 2.2 9901 9904 9906 9936 2.4 3896 9898 2931 993 9934 2.3 9893 9925 9927 9929 9952 2.5 9922 24 9918 ozbe 9948 .9949 9951 .9943 9945 .9946 9963 9964 2.6 9940 9941 9962 2.5 9938 .9957 .9959 9960 9961 9973 9974 2.7 9972 2.6 9955 9956 9953 9971 9967 9968 9969 .9970 9981 2.8 9980 27 9965 3966 .9978 .9979 9979 .9977 9977 9986 2.9 9976 9986 28 9974 9975 .9984 .9984 .9985 9985 2990 3.0 .9983 3982 9982 .9989 9989 9990 2.9 9981 9987 9988 9988 .9989 3.1 2987 9992 9993 9993 3.0 9987 .9991 .9992 .9992 .9992 9995 9995 3.2 9990 9991 9991 9994 +666' 9995 3.1 .9994 .9994 9996 9997 3.3 3.2 .9993 9993 9994 9996 .9996 9995 9996 9996 .9996 34 9997 9998 9995 9997 .9997 9097 3.3 9995 9097 .9997 3.50 and up 9997 9097 34 9997 08 09 9999 05 .06 07 3.50 and up 03 04 00 02 Common Critical Values NOTE: For values of z above 3.49, use 0.9999 for the area. Canfirlenna Critical 1/2 https://mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=627 170671&questionId=1&flushed=false&cld=6988267¢erwin=yes Cumulative area to the left of positive z scores 11/8/22, 12:56 AM Level Value 0.90 1.645 Use these common values that result from interpolation: 0.95 1.96 0.99 2.575 z Score Area 1.645 0.9500 2.575 0.9950 2/2 https://mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=627 170671&questionId=1&flushed=false&cld=6988267¢erwin=yes11/8/22, 12:55 AM Critical t values t Distribution: Critical t Values Left tail Area in One Tail 0.005 0.01 0.025 0.05 0.10 Degrees of Area in Two Tails Degrees of Freedom 0.01 0.02 0.05 0.10 0.20 Freedom 63.657 31.821 12.706 6.314 3.078 2 9.925 6.965 4.303 2.920 1.886 3 5.841 4.541 3.182 2.353 1.638 4.604 3.747 2.776 2.132 1.533 4.032 3.365 2.571 2.015 1.476 6 3.707 3.143 2.447 1.943 1.440 3.499 2.998 2.365 1.415 3.355 2.896 2.306 1.397 9 3.250 2.821 2.262 1.833 1.383 Critical t value 10 3.169 2.764 2.228 1.812 1.372 10 (negative) 11 3,106 2.718 2.201 1.796 1.363 11 12 3.055 2.681 2.179 1.782 1.356 12 13 3.012 2.650 2.160 1.771 1.350 13 14 2.977 2.624 2.145 1.761 1.345 14 15 2 947 2.602 2.131 1.753 1.341 15 Right tail 16 2.921 2.583 2.120 1.746 1.337 16 17 2.898 2.567 2.110 1.740 1.333 17 18 2.878 2.552 2.101 1.734 1.330 18 19 2.861 2.539 2.093 1.729 1.328 19 20 2.845 2.528 2.086 1.725 1.325 20 21 2.831 2.518 2.080 1.721 1.323 21 22 2.819 2.508 2.074 1.717 1.321 22 23 2807 2.500 2.069 1.714 1.319 23 24 2.797 2.492 2.064 1.711 1.318 25 2.787 2.485 2.060 1.708 1.316 25 26 2.779 2.479 2.056 1.706 1.315 26 27 2.771 2.473 2.052 1,703 1.314 27 Critical t value 28 2.763 2.467 2.048 1.701 1.313 28 (positive) 29 2.756 2.462 2.045 1.699 1.311 29 30 2.750 2.457 2.042 1.697 1.310 30 31 2.744 2.453 2.040 1.696 1.309 31 32 2.738 2.449 2.037 1.694 1.309 32 33 2.733 2.445 2.035 1.692 1.308 33 34 2.728 2.441 2.032 1.691 1.307 34 35 2.724 2.438 2.030 1.690 1.306 35 36 2.719 2.434 2.028 1.688 1.306 36 Two tails 37 2.715 2.431 2.026 1.687 1.305 37 38 2.712 2.429 2.024 1.686 1.304 38 39 2.708 2.426 2.023 1.685 1.304 39 40 2.704 2.423 2.021 1.684 1.303 40 45 2.690 2.412 2.014 1.679 1.301 45 50 2.678 2.403 2.009 1.676 1.299 50 60 2.660 2.390 2.000 1.671 1.296 60 70 2.648 2.381 1.994 1.667 1.294 70 a/2 a/2 80 2.639 2.374 1.990 1.664 1.292 80 2.632 2.368 1.987 1.662 1.291 90 100 2.626 2.364 1.984 1.660 1.290 100 200 2.601 2.345 1.972 1.653 1.286 200 Critical t value Critical t value 300 2.592 2.339 1.968 1.650 1.284 300 (negative) (positive) 400 2.588 2.336 1.966 1.649 1.284 400 500 2.586 2.334 1.965 1.648 1.283 500 1000 2.581 2.330 1.962 1.646 1.282 1000 2000 2.578 2.328 1.961 1.646 1.282 2000 2 576 2 326 1 645 1 2RD Lame https://mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=627 170671&questionId=1&flushed=false&cld=6988267¢erwin=yes 1/2 11/8/22, 12:55 AM Critical t values LA yu Area in One Tail 0.005 0.01 0.025 0.05 0.10 Degrees of Area in Two Tails Degrees of Freedom 0.01 0.02 0.05 0.10 0.20 Freedom https://mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=627 170671&questionId=1&flushed=false&cld=6988267¢erwin=yes 2/2A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 16 subjects had a mean wake time of 105.0 min. After treatment, the 16 subjects had a mean wake time of 100.1 min and a standard deviation of 22.5 min. Assume that the 16 sample values appear to be from a normally distributed population and construct a 90% condence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 105.0 min before the treatment? Does the drug appear to be effective? In a test of the effectiveness of garlic for lowering cholesterol, 44 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before - after) in their levels of LDL cholesterol (in mgldL) have a mean of 5.6 and a standard deviation of 17.1. Construct a 99% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the condence interval suggest about the effectiveness of garlic in reducing LDL cholesterol? Click here to view a t distribution table. Click here to view @9e 1 of the standard normal distribution table. umammmnmmmmmmnmmmmmam A food safety guideline is that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 90% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi? 0.55 0.78 0.10 0.86 1.38 0.54 0.96A food safety guideline is that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 90% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi? 0.55 0.78 0.10 0.86 1.38 0.54 0.96Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 95% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required? 249 218 185 170 168 156 156 156 156 154An IQ test is designed so that the mean is 100 and the standard deviation is 10 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 7 IQ points of the true mean. Assume that o = 10 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. (3 The required sample size is D. (Round up to the nearest integer.) Assume that all gradepoint averages are to be standardized on a scale between 0 and 6. How many gradepoint averages must be obtained so that the sample mean is within 0.006 of the population mean? Assume that a 95% range 6 - 0 = = 1.5. Does the confidence level is desired. If using the range rule of thumb, 0' can be estimated as 4 4 sample size seem practical? The ages of a group of 151 randomly selected adult females have a standard deviation of 17.8 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let 0 = 17.8 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 99% confidence that the sample mean is within onehalf year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population