Stat 200 Assignment 1 Problem #1: A stylist at the Hair Care Palace gathered data on the number of hair colourings given on Saturdays and on weekdays. Her results are listed below. Assume the two random samples were independently taken from normal populations. Saturday: = 50 and Weekday: = 14 65 and 2 = 13 a) Find the point estimate of p1 - p2 and the 95% margin of error. POINTS: 5 b) Estimate the difference in the true proportions with a 99% confidence interval. Interpret this interval. POINTS: 5 Problem #2: Independent random samples of = 150 and =150, sales phone calls for an insurance policy were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 80 successful sales, and sample 2 had 88 successful sales. a) Suppose you have no preconceived theory concerning which parameter, Por Paris the larger and you wish to detect only a difference between the two parameters if one exists. What should you choose as the null and alternative hypotheses for a statistical test? POINTS: 2 b) Calculate the standard error of the difference in the two sample proportions (P - P) Make sure to use the pooled estimate for the common value of p. POINTS: 3 c) Calculate the test statistic of P- Pa. Based on your knowledge of the standard normal distribution, is this a 10 is true and the two population proportions are the same? likely or an unlikely observation, assuming that Justify your conclusion. Hoi POINTS: 3 d) Use the critical value approach to find the rejection region when a = 0.01. Do the data provide sufficient evidence to indicate a difference in the population proportions? POINTS: 2 e) Find the p-value for the test. Test for a significant difference in the population means at the 1% significance level. POINTS: 2 Normal Curve Areas P(z < 1.23) = Area 0.8907 Z 0.02 0 1.23 0.04 0.05 0.06 0.0003 2 0.00 0.01 0.03 0.07 0.08 0.09 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 2 0.00 0.03 0.04 0.05 0.06 0.07 0.08 0.01 0.02 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.2 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901 0.9901 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 Student's t Distribution (Critical Values) 1- a -t t Left-tailed Test Right-tailed Test -t Two-tailed Test t t -t Confidence Interval Confidence Coefficient, 1-a 0.80 0.90 df 0.95 Level of Significance for One-Tailed Test, a 0.100 0.050 0.025 0.010 0.005 0.98 0.99 0.999 df 0.0005 Level of Significance for Two-Tailed Test, a Confidence Coefficient, 1-a 0.80 0.90 0.95 0.98 0.99 0.999 Level of Significance for One-Tailed Test, a 0.100 0.050 0.025 0.010 0.005 0.0005 Level of Significance for Two-Tailed Test, a 0.20 0.10 0.05 0.02 0.01 0.001 0.20 0.10 0.05 0.02 0.01 0.001 12315 3.078 6.314 12.706 31.821 63.657 1.886 2.920 4.303 6.965 9.925 1.638 2.353 3.182 4.541 5.841 1.533 2.132 2.776 3.747 4.604 1.476 2.015 2.571 3.365 4.032 636.619 31.599 12.924 31 32 33 1.308 1.309 1.696 2.040 2.453 2.744 3.633 1.309 1.694 2.037 2.449 2.738 3.622 1.692 2.035 2.445 2.733 3.611 8.610 34 1.307 1.691 2.032 2.441 2.728 3.601 6.869 35 1.306 1.690 2.030 2.438 2.724 3.591 08129 6 1.440 1.943 2.447 3.143 3.707 5.959 36 1.306 1.688 2.028 2.434 2.719 3.582 7 1.415 1.895 2.365 1.397 1.860 2.306 2.896 1.383 1.833 2.262 2.821 1.372 1.812 2.228 2.764 2.998 3.499 5.408 37 1.305 1.687 2.026 2.431 2.715 3.574 3.355 5.041 38 1.304 1.686 2.024 2.429 2.712 3.566 3.250 4.781 3.169 4.587 39 40 1.304 1.303 1.685 2.023 2.426 2.708 1.684 2.021 3.558 2.423 2.704 3.551 11 1.363 1.796 2.201 2.718 3.106 12 1.356 1.782 2.179 2.681 3.055 4.437 4.318 42 13 1.350 1.771 2.160 2.650 3.012 4.221 43 14 1.345 1.761 15 1.341 1.753 2.145 2.131 2.624 2.977 2.602 2.947 4.140 4.073 12345 41 1.303 1.683 2.020 2.421 2.701 1.302 1.682 2.018 2.418 2.698 1.302 1.681 2.017 2.416 2.695 3.544 3.538 3.532 44 1.301 1.680 2.015 2.414 2.692 45 1.301 1.679 2.014 2.412 2.690 3.526 3.520 STLOO 20 1.325 1.725 16 1.337 1.746 2.120 2.583 2.921 17 1.333 1.740 2.110 2.567 2.898 18 1.330 1.734 2.101 2.552 2.878 19 1.328 1.729 2.093 2.086 4.015 3.965 3.922 2.539 2.861 2.528 2.845 3.883 3.850 9149 46 1.300 1.679 2.013 2.410 2.687 3.515 47 1.300 1.678 2.012 2.408 2.685 3.510 48 1.299 1.677 2.011 2.407 2.682 3.505 49 1.299 1.677 2.010 2.405 2.680 3.500 50 1.299 1.676 2.009 2.403 2.678 3.496 21 1.323 1.721 2.080 2.518 223 22 1.321 1.717 2.074 2.508 23 1.319 1.714 2.069 2.500 2.807 2.831 2.819 3.819 51 3.792 3.768 24 1.318 1.711 25 1.316 1.708 2.064 2.492 2.060 2.485 2.797 2.787 3.745 3.725 1.298 1.675 2.008 2.402 2.676 3.492 52 1.298 1.675 2.007 2.400 2.674 3.488 53 1.298 1.674 2.005 2.399 54 1.297 1.674 2.005 2.397 55 1.297 1.673 2.004 2.396 2.668 3.476 2.672 3.484 2.670 3.480 2222 26 27 1.315 1.706 2.056 2.479 2.779 1.314. 1.703 2.052 2.473 2.771 28 1.313 1.701 2.048 2.467 2.763 29 1.311 1.699 2.045 2.462 2.756 30 1.310 1.697 2.042 2.457 2.750 3.707 3.690 3.674 3.659 3.646 60 1.296 1.671 2.000 2.390 2.660 3.460 80 1.292 1.664 1.990 2.374 2.639 3.416 100 1.290 1.660 1.984 2.364 2.626 3.390 200 1.286 1.653 1.972 2.345 2.601 3.340 1.282 1.645 1.960 2.326 2.576 3.291