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 96.58 101.9 106.6 108.1 112.3 116.3 120.1 124.8 100 109.1 111.7 114.7 118.5 124.3 129.6 131.1 135.8 140.2 144.3 149.4D DIRECTIONS: Use this information for questions 23 and 24. Suppose it is known that the mean number of points scored by the Spurs last season is 91, with a standard deviation of 7.2 and the mean number of points scored by the Warriors last season is 96, with a standard deviation of 4.2. Erica and her classmate, Cal chose 30 games from each team to examine. D Question 23 1 pts Which of these tells us that a normal distribution is a reasonable model for this problem? The Chi-squared distribution O The Empirical Rule The two sample t-test The Central Limit Theorem Matched pairs designMatched pairs design D Question 24 1 pts Erica and Cal wish to approximate the probability that the sample mean from each team is within 2 points of one another. Each student used a normal cumulative distribution function, but entered different arguments, as shown in the table below. Erica Cal normalcdf(-4.60, -1.97, 0, 1) = 0.024 normalcdf(-2, 2, 5, 1.52) = 0.024 Which of the following best describes the students' work? O Both students are correct. Cal used z-scores and the standard normal distribution, but Erica used the values from the problem. O Both students are correct. Erica used z-scores and the standard normal distribution, but Cal used the values from the problem. O Both students are incorrect. Their arguments are correct, but the correct value is not 0.024. O Erica's method is correct because she used z-scores. Cal's method is not correct. O Cal's method is correct because he used u = 5 and o = 1.52. Erica's method is not correct.