One of the tasks in data mining is association rule mining. It is concerned with the discovery of associations and correlations between (frequent) itemsets in a given transactional data. 1. Given a dataset of ten transactions, a minimum support threshold of 30% and a minimum confidence threshold of 70%, a. Find all the frequent itemsets using the Apriori algorithm. b. Find all the strong association rules from the frequent itemsets obtained from the previous question. 2. Given the following dataset containing fifteen (15) transactions. a. Find the frequent itemsets. Let's assume the minimum support is 25%. b. Find the support and confidence for all possible association rules. Refer to the following statistics. Calculate the support an confidence for the given association rules: 100,000 transactions 3,000 transactions contain beef 10,000 transactions contain fish 5,000 transactions contain poultry 7,000 transactions contain both beef \& poultry 7,000 transactions contain both fish & beef 8,000 transactions contain both fish \& poultry 60,000 transactions contain beef, fish \& poultry Chi-Square Follow the steps for a chi-square test for the following situations: 1. Given the survey results of 1500 respondents about their preference for science fiction. (significant level is 0.001 ) 2. Given the following observation of 100 respondents who deposits garbage into the garbage bin or simply litters. (significant level is 0.001 ) 3. A group of young adults were classified in terms of personality (introvert or extrovert) and in terms of their colour preferences (red, green, blue or yellow). The observed count is shown in the following table. (Assume significance level is 0.001 ) Table 1 : Observed counts of colour with respect to personality \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multirow[b]{2}{*}{ df } & \multicolumn{12}{|c|}{ Tail probability p} \\ \hline & .25 & .20 & .15 & .10 & .05 & .025 & .02 & .01 & .005 & .0025 & .001 & .0005 \\ \hline 1 & 1.32 & 1.64 & 2.07 & 2.71 & 3.84 & 5.02 & 5.41 & 6.63 & 7.88 & 9.14 & 10.83 & 12.12 \\ \hline 2 & 2.77 & 3.22 & 3.79 & 4.61 & 5.99 & 7.38 & 7.82 & 9.21 & 10.60 & 11.98 & 13.82 & 15.20 \\ \hline 3 & 4.11 & 4.64 & 5.32 & 6.25 & 7.81 & 9.35 & 9.84 & 11.34 & 12.84 & 14.32 & 16.27 & 17.73 \\ \hline 4 & 5.39 & 5.99 & 6.74 & 7.78 & 9.49 & 11.14 & 11.67 & 13.28 & 14.86 & 16.42 & 18.47 & 20.00 \\ \hline 5 & 6.63 & 7.29 & 8.12 & 9.24 & 11.07 & 12.83 & 13.39 & 15.09 & 16.75 & 18.39 & 20.51 & 22.11 \\ \hline 6 & 7.84 & 8.56 & 9.45 & 10.64 & 12.59 & 14.45 & 15.03 & 16.81 & 18.55 & 20.25 & 22.46 & 24.10 \\ \hline 7 & 9.04 & 9.80 & 10.75 & 12.02 & 14.07 & 16.01 & 16.62 & 18.48 & 20.28 & 22.04 & 24.32 & 26.02 \\ \hline 8 & 10.22 & 11.03 & 12.03 & 13.36 & 15.51 & 17.53 & 18.17 & 20.09 & 21.95 & 23.77 & 26.12 & 27.87 \\ \hline 9 & 11.39 & 12.24 & 13.29 & 14.68 & 16.92 & 19.02 & 19.68 & 21.67 & 23.59 & 25.46 & 27.88 & 29.67 \\ \hline 10 & 12.55 & 13.44 & 14.53 & 15.99 & 18.31 & 20.48 & 21.16 & 23.21 & 25.19 & 27.11 & 29.59 & 31.42 \\ \hline 11 & 13.70 & 14.63 & 15.77 & 17.28 & 19.68 & 21.92 & 22.62 & 24.72 & 26.76 & 28.73 & 31.26 & 33.14 \\ \hline 12 & 14.85 & 15.81 & 16.99 & 18.55 & 21.03 & 23.34 & 24.05 & 26.22 & 28.30 & 30.32 & 32.91 & 34.82 \\ \hline 13 & 15.98 & 16.98 & 18.20 & 19.81 & 22.36 & 24.74 & 25.47 & 27.69 & 29.82 & 31.88 & 34.53 & 36.48 \\ \hline 14 & 17.12 & 18.15 & 19.41 & 21.06 & 23.68 & 26.12 & 26.87 & 29.14 & 31.32 & 33 & 36.12 & 38.11 \\ \hline 15 & 18.25 & 19.31 & 20.60 & 22.31 & 25.00 & 27.49 & 28.26 & 30.58 & 32.80 & 34.95 & 37.70 & 39.72 \\ \hline 16 & 19.37 & 20.47 & 21.79 & 23.54 & 26.30 & 28.85 & 29.63 & 32.00 & 34.27 & 36.46 & 39.25 & 41.31 \\ \hline 17 & 20.49 & 21.61 & 22.98 & 24.77 & 27.59 & 30.19 & 31.00 & 33.41 & 35.72 & 37.95 & 40.79 & 42.88 \\ \hline 18 & 21.60 & 22.76 & 24.16 & 25.99 & 28.87 & 31.53 & 32.35 & 34.81 & 37.16 & 39.42 & 42.31 & 44.43 \\ \hline 19 & 22.72 & 23.90 & 25.33 & 27.20 & 30.14 & 32.85 & 33.69 & 36.19 & 38.58 & 40.88 & 43,82 & 45.97 \\ \hline 20 & 23.83 & 25.04 & 26.50 & 28.41 & 31.41 & 34.17 & 35.02 & 37.57 & 40.00 & 42.34 & 45.31 & 47.50 \\ \hline 21 & 24.93 & 26.17 & 27.66 & 29.62 & 32.67 & 35.48 & 36.34 & 38.93 & 41.40 & 43.78 & 46.80 & 49.01 \\ \hline 22 & 26.04 & 27.30 & 28.82 & 30.81 & 33.92 & 36.78 & 37.66 & 40.29 & 42.80 & 45.20 & 48.27 & 50.51 \\ \hline 23 & 27.14 & 28.43 & 29.98 & 32.01 & 35.17 & 38.08 & 38.97 & 41.64 & 44.18 & 46.62 & 49.73 & 52.00 \\ \hline 24 & 28.24 & 29.55 & 31.13 & 33.20 & 36.42 & 39.36 & 40.27 & 42.98 & 45.56 & 48.03 & 51.18 & 53.48 \\ \hline 25 & 29.34 & 30.68 & 32.28 & 34.38 & 37.65 & 40.65 & 41.57 & 44.31 & 46.93 & 49.44 & 52.62 & 54.95 \\ \hline 26 & 30.43 & 31.79 & 33.43 & 35.56 & 38.89 & 41.92 & 42.86 & 45.64 & 48.29 & 50.83 & 54.05 & 56.41 \\ \hline 27 & 31.53 & 32.91 & 34.57 & 36.74 & 40.11 & 43.19 & 44.14 & 46.96 & 49.64 & 52.22 & 55.48 & 57.86 \\ \hline 28 & 32.62 & 34.03 & 35.71 & 37.92 & 41.34 & 44.46 & 45.42 & 48.28 & 50.99 & 53.59 & 56.89 & 59.30 \\ \hline 29 & 33.71 & 35.14 & 36.85 & 39.09 & 42.56 & 45.72 & 46.69 & 49.59 & 52.34 & 54.97 & 58.30 & 60.73 \\ \hline 30 & 34.80 & 36.25 & 37.99 & 40.26 & 43.77 & 46.98 & 47.96 & 50.89 & 53.67 & 56.33 & 59.70 & 62.16 \\ \hline 40 & 45.62 & 47.27 & 49.24 & 51.81 & 55.76 & 59.34 & 60.44 & 63.69 & 66.77 & 69.70 & 73.40 & 76.09 \\ \hline 50 & 56.33 & 58.16 & 60.35 & 63.17 & 67.50 & 71.42 & 72.61 & 76.15 & 79.49 & 82.66 & 86.66 & 89.56 \\ \hline 60 & 66.98 & 68.97 & 71.34 & 74.40 & 79.08 & 83.30 & 84.58 & 88.38 & 91.95 & 95.34 & 99.61 & 102.7 \\ \hline 80 & 88.13 & 90.41 & 93.11 & 96.58 & 101.9 & 106.6 & 108.1 & 112.3 & 116.3 & 120.1 & 124.8 & 128.3 \\ \hline 100 & 109.1 & 111.7 & 114.7 & 118.5 & 124.3 & 129.6 & 131.1 & 135.8 & 140.2 & 144.3 & 149.4 & 153.2 \\ \hline \end{tabular}