This is statistics course, sampling distributions, estimation and tests of significance units.I need help with this. I attached formula sheet in case you need it.

II. Probability P(AUB) = P(A) + P(B) - P(An B) P(AB) = P(An B) P(B) E(X) = Ux = Expi Var(X) = 0; = _(x - ux)2pi If X has a binomial distribution with parameters n and p, then: P(X = k) = k) p* (1 - p)" -* HI = np Or = Vnp(1 - p) Ho = P Op = P(1- p n If x is the mean of a random sample of size n from an infinite population with mean u and standard deviation O, then: MY = HIII. Inferential Statistics Standardized test statistic: statistic - parameter standard deviation of statistic Confidence interval: statistic + (critical value) . (standard deviation of statistic) Single-Sample Statistic Standard Deviation of Statistic Sample Mean Sample Proportion p(1 - p) n Two-Sample Statistic Standard Deviation of Statistic Difference of sample means 722 Special case when 61 =02 ol+1 n2 Difference of PI (1 - PI) + P2 (1 - P2) sample proportions n1 n2 Special case when P1 = P2 Jp(1 - P) 1 + 1 Vn, n2 Chi-square test statistic = \\ (observed - expected) expected\fTable entry for p and C is the point t* with probability p lying above it Probability p and probability C lying between -t* and t*. Table B t distribution critical values Tail probability p df .25 .20 .15 .10 05 .025 .02 .01 .005 0025 .001 .0005 1.000 1.376 1.963 3.078 6.314 12.71 15.89 31.82 63.66 127.3 318.3 636.6 .816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.09 22.33 31.60 .765 978 1.250 1.638 2.353 3.182 3.482 4.541 5.841 7.453 10.21 12.92 .741 .941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 5.598 7.173 8.610 .727 920 1.156 1.476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.869 .718 906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959 .711 .896 1.119 1.415 1.895 2.365 2.517 2.998 3.499 4.029 4.785 5.408 .706 889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041 1703 883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 10 700 879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 .697 .876 1.088 1.363 1.796 2.201 2.328 2.718 3.106 3.497 4.025 4.437 12 695 873 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 13 694 870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.221 14 .692 868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 15 691 866 1.074 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 16 .690 865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.015 689 863 1.069 1.333 1.740 2.110 2.224 2.567 2.898 3.222 3.646 3.965 18 688 862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.611 3.922 19 .688 .861 1.066 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 20 687 860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 3.850 21 686 859 1.063 1.323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819 686 .858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792 23 685 858 1.060 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485 3.768 24 685 857 1.059 1.318 1.711 2.064 2.172 2.492 2.797 3.091 3.467 3.745 25 .684 856 1.058 1.316 1.708 2.060 2.167 2.485 2.787 3.078 3.450 3.725 26 .684 856 1058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707 27 684 855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 3.057 3.421 3.690 28 683 855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.408 3.674 29 683 .854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 3.038 3.396 3.659 30 .683 .854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646 40 .681 .851 1.050 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551 50 .679 .849 1.047 1.299 1.676 2.009 2.109 2.403 2.678 2.937 3.261 3.496 60 .679 .848 1.045 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 3.460 80 .678 .846 1.043 1.292 1.664 1.990 2.088 2.374 2.639 2.887 3.195 3.416 100 .677 .845 1.042 1.290 1.660 1.984 2.081 2.364 2.626 2.871 3.174 3.390 1000 .675 .842 1.037 1.282 1.646 1.962 2.056 2.330 2.581 2.813 3.098 3.300 .674 841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.091 3.291 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% Confidence level CTable entry Probability p for p is the point (x ) with probability p lying above it. (x2) Table C * critical values Tail probability p df .25 .20 .15 .10 05 025 .02 .01 .005 .0025 001 1 1.32 1.64 2.07 2.71 3.84 5.02 5.41 6.63 7.88 9.14 10.83 2.77 3.22 3.79 4.61 5.99 7.38 7.82 9.21 10.60 11.98 13.82 4.11 4.64 5.32 6.25 7.81 9.35 9.84 11.34 12.84 14.32 16.27 5.39 5.99 6.74 7.78 9.49 11.14 11.67 13.28 14.86 16.42 18.47 6.63 7.29 8.12 9.24 11.07 12.83 13.39 15.09 16.75 18.39 20.51 7.84 8.56 9.45 10.64 12.59 14.45 15.03 16.81 18.55 20.25 22.46 9.04 9.80 10.75 12.02 14.07 16.01 16.62 18.48 20.28 22.04 24.32 10.22 11.03 12.03 13.36 15.51 17.53 18.17 20.09 21.95 23.77 26.12 11.39 12.24 13.29 14.68 16.92 19.02 19.68 21.67 23.59 25.46 27.88 12.55 13.44 14.53 15.99 18.31 20.48 21.16 23.21 25.19 27.11 29.59 11 13.70 14.63 15.77 17.28 19.68 21.92 22.62 24.72 26.76 28.73 31.26 12 14.85 15.81 16.99 18.55 21.03 23.34 24.05 26.22 28.30 30.32 32.91 13 15.98 16.98 18.20 19.81 22.36 24.74 25.47 27.69 29.82 31.88 34.53 14 17.12 18.15 19.41 21.06 23.68 26.12 26.87 29.14 31.32 33.43 36.12 15 18.25 19.31 20.60 22.31 25.00 27.49 28.26 30.58 32.80 34.95 37.70 16 19.37 20.47 21.79 23.54 26.30 28.85 29.63 32.00 34.27 36.46 39.25 17 20.49 21.61 22.98 24.77 27.59 30.19 31.00 33.41 35.72 37.95 40.79 18 21.60 22.76 24.16 25.99 28.87 31.53 32.35 34.8 37.16 39.42 42.31 19 22.72 23.90 25.33 27.20 30.14 32.85 33.69 36.19 38.58 40.88 43.82 20 23.83 25.04 26.50 28.41 31.41 34.17 35.02 37.57 40.00 42.34 45.31 21 24.93 26.17 27.66 29.62 32.67 35.48 36.34 38.93 41.40 43.78 46.80 22 26.04 27.30 28.82 30.81 33.92 36.78 37.66 40.29 42.80 45.20 48.27 23 27.14 28.43 29.98 32.01 35.17 38.08 38.97 1.64 44.18 46.62 49.73 24 28.24 29.55 31.13 33.20 36.42 39.36 40.27 42.98 45.56 48.03 51.18 25 29.34 30.68 32.28 34.38 37.65 40.65 41.57 44.31 46.93 49.44 52.62 26 30.43 31.79 33.43 35.56 38.89 41.92 42.86 45.64 48.29 50.83 54.05 27 31.53 32.91 34.57 36.74 40.11 43.19 44.14 46.96 49.64 52.22 55.48 28 32.62 34.03 35.71 37.92 41.34 44.46 45.42 48.28 50.99 53.59 56.89 29 33.71 35.14 36.85 39.09 42.56 45.72 46.69 49.59 52.34 54.97 58.30 30 34.80 36.25 37.99 40.26 43.77 46.98 47.96 50.89 53.67 56.33 59.70 40 45.62 47.27 49.24 51.8 55.76 59.34 60.44 63.69 66.77 69.70 73.40 50 56.33 58.16 60.35 63.17 67.50 71.42 72.61 76.15 79.49 82.66 86.66 60 66.98 68.97 71.34 74.40 79.08 83.30 84.58 88.38 91.95 95.34 99.61 80 88.13 90.41 93.11 96.58 101.9 106.6 108.1 112.3 116.3 120.1 124.8 100 109.1 111.7 114.7 118.5 124.3 129.6 131.1 135.8 140.2 144.3 149.4\fD Question 48 1 pts Suppose a 95% confidence interval is constructed for the difference of two proportions and is found by the expression 0.05 + (1.96)(0.066). Which of these is NOT true? O The difference in proportions for the populations is 0.05. The critical z value is 1.96. The standard deviation is 0.066. The confidence interval is approximately (-0.08, 0.18). O The margin of error is approximately 0.13.D Question 50 1 pts A study was conducted to see if there is a difference between the perceptions of Illinois residents who live in rural communities versus urban communities as to whether or not their education sufficiently prepared them for their careers. At random, 1,500 Illinois residents were selected to participate. The results of the study are shown below. Type of Community Rural Urban Total Yes 422 576 998 Do you believe that your education No 160 342 528 sufficiently prepared you for your career? Total 582 918 1500 We wish to use the survey to test the hypothesis that the proportion of rural Illinois residents who think their education is sufficient is the same as the proportion of urban Illinois residents who think their education is sufficient. Which of these is NOT an appropriate test or condition for this situation? O Two sample proportion z-test The sample size must be greater than or equal to 50 The two samples must be independent of each other The two populations must be at least 10 times larger than their samples There must be at least 10 successes and 10 failures in each sample