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Question 1 g 10 marks! The education department has conducted a survey to review student's language ability. A sample of 40 boys and 40 girls have been selected randomly selected for an aptitude test. The test result is that 28 boys pass the test, and 32 girls pass the test. (a) Give a point estimate of the population proportion of boys can pass the aptitude test. (1)) Give a point estimate of the population proportion of girls can pass the aptitude test. (c) Use the combined data of 80 students, give a point estimate of the population proportion of students can pass the aptitude test. ((1) Use the combined data of 80 students, construct a 95% condence interval estimate of the population proportion of students can pass the aptitude test. The entries in Table I are the probabilities that a random variable having the standard normal distribution will take on a value between 0 andz. They are given by the area of the gray region under the curve in the gure. 0.00 0.0000 0.0398 0.0793 0. 1 l 79 0.1554 0.1915 0.2257 0.2580 0.2881 0.3 159 0.3413 0.3643 0.3849 0.4032 0.4192 0.4332 0.4452 0.4554 0.4641 0.4713 0.4772 0.4821 0.4861 0.4893 0.4918 0.4938 0.4953 0.4965 0.4974 0.4981 0.4987 0.01 0.0040 0.0438 0.0832 0. l2 1 7 0.1591 0.1950 0.2291 0.261 1 0.2910 0.3186 0.3438 0.3665 0.3869 0.4049 0.4207 0.4345 0.4463 0.4564 0.4648 0.4719 0.4778 0.4826 0.4864 0.4896 0.4920 0.4940 0.4955 0.4966 0.4975 0.4982 0.4987 TABLE I 0.02 0.03 0.0080 0.0120 0.0478 0.0517 0.0871 0.0910 0. 1255 0. 1293 0. 1628 0. 1664 0.1985 0.2019 0.2324 0.2357 0.2642 0.2673 0.2939 0.2967 0.3212 0.3238 0.3461 0.3485 0.3686 0.3708 0.3888 0.3907 0.4066 0.4082 0.4222 0.4236 0.4357 0.4370 0.4474 0.4484 0.4573 0.4582 0.4656 0.4664 0.4725 0.4732 0.4783 0.4788 0.4830 0.4834 0.4868 0.4871 0.4898 0.4901 0.4922 0.4925 0.4941 0.4943 0.4956 0.4957 0.4967 0.4968 0.4976 0.4977 0.4982 0.4983 0.4987 0.4988 NORMAL-CURVE AREAS 0.04 0.05 0.06 0.0160 0.0199 0.0239 0.0557 0.0596 0.0636 0.0948 0.0987 0.1026 0.1331 0.1368 0.1406 0.1700 0.1736 0.1772 0.2054 0.2088 0.2123 0.2389 0.2422 0.2454 0.2704 0.2734 0.2764 0.2995 0.3023 0.3051 0.3264 0.3289 0.3315 0.3508 0.3531 0.3554 0.3729 0.3749 0.3770 0.3925 0.3944 0.3962 0.4099 0.4115 0.4131 0.4251 0.42 65 0.4279 0.4382 0.4394 0.4406 0.4495 0.4505 0.45 15 0.4591 0.4599 0.4608 0.4671 0.4678 0.4685 0.4738 0.4744 0.4750 0.4793 0.4798 0.4803 0.4838 0.4842 0.4846 0.4875 0.48 78 0.4881 0.4904 0.4906 0.4909 0.4927 0.4929 0.4931 0.4945 0.4946 0.4948 0.4959 0.4960 0.4961 0.4969 0.4970 0.4971 0.4977 0.4978 0.4979 0.4984 0.4984 0.4985 0.4988 0.4989 0.4989 Also. for z =4.0, 5.0 and 6.0. the areas are 0.49997. 0.4999997, and 0.499999999. 0.07 0.0279 0.0675 0.1064 0.1443 0.1808 0.2157 0.2486 0.2794 0.3078 0.3340 0.3577 0.3790 0.3980 0.4147 0.4292 0.4418 0.4525 0.4616 0.4692 0.4756 0.4808 0.4850 0.4884 0.491 1 0.4932 0.4949 0.4962 0.4972 0.4979 0.4985 0.4989 0.08 0.03 19 0.0714 0. l 103 0. 1480 0. 1844 0.2190 0.2517 0.2823 0.3106 0.3365 0.3599 0.3810 0.3997 0.4162 0.4306 0.4429 0.4535 0.4625 0.4699 0.4761 0.4812 0.4854 0.4887 0.4913 0.4934 0.495 1 0.4963 0.4973 0.4980 0.4986 0.4990 0.09 0.0359 0.0753 0. l 14 1 0. l5 1 7 0. 1879 0.2224 0.2549 0.2852 0.3133 0.33 89 0.3621 0.3830 0.4015 0.4177 0.43 19 0.4441 0.4545 0.4633 0.4706 0.4767 0.4817 0.4857 0.4890 0.4916 0.4936 0.4952 0.4964 0.4974 0.4981 0.4986 0.4990 The entries in Table II are values for which the area to their right under the distribution with given degrees of freedom (the gray area in the figure) is equal to a . TABLE II VALUE OF d.f. 0.050 to.025 10.010 10.005 d.f. 6.314 12.706 31.821 63.657 2.920 4.303 6.965 9.925 N UAWN - 2.353 3.182 4.541 5.84 A W 2.132 2.776 3.747 4.604 2.015 2.571 3.365 4.032 1.943 2.447 3.143 3.707 1.895 2.365 2.998 3.499 1.860 2.306 2.896 3.355 1.833 2.262 2.821 3.250 1.812 2.228 2.764 3.169 11 1.796 2.201 2.718 3.106 11 12 1.782 2.179 2.681 3.055 12 1.771 2.160 2.650 3.012 13 14 1.761 2.145 2.624 2.977 14 15 1.753 2.131 2.602 2.947 15 16 1.746 2.120 2.583 2.921 16 17 1.740 2.110 2.567 2.898 17 18 1.734 2.101 2.552 2.878 18 19 1.729 2.093 2.539 2.861 19 20 1.725 2.086 2.528 2.84 20 21 1.721 2.080 2.518 2.831 21 22 1.717 2.074 2.508 2.819 22 23 1.714 2.069 2.500 2.807 23 24 1.711 2.064 2.492 2.797 24 25 1.708 2.060 2.485 2.787 25 26 1.706 2.056 2.479 2.779 26 27 1.703 2.052 2.473 2.771 27 28 1.701 2.048 2.467 2.763 28 29 1.699 2.045 2.462 2.756 29 Inf. 1.645 1.960 2.326 2.576 Inf