Test of Hypotheses: Part 1 Problem: 1 A random sample of 13 milk packets was taken from a dairy company. Detected amount of lead was 0.02, 0.05, 0.06, 0.008, 0.072, 0.11, 0.01, 0.006, 0.05, 0.03, 0.07, 0.004 and 0.002 milligram per kilogram respectively. Test the hypothesis that the average of the selected sample units lies within the maximum permissible limit of lead in milk (0.02 milligram per kilogram) at 5% level of significance. Problem: 2 A random sample of 10 drinking water bottles has been selected for water safety research. Quantity of observed arsenic are 10, 9, 12, 14, 8, 11, 10, 13, 9 and 13 ug/L respectively. Test the hypothesis that the average arsenic content of the bottle is 10 ug/L at 1% level of significance.Problem 1: Basic statistics: Frequency distribution Food hygiene scores obtained by 60 restaurants in Dhaka-North are given below: 35 36 29 40 31 17 15 18 33 27 38 15 33 34 41 26 16 25 33 36 24 22 26 19 36 18 25 20 25 25 31 24 16 28 30 24 76 42 29 88 26 27 47 43 22 28 28 22 24 23 55 65 76 34 45 28 89 49 31 58 Describe the performance of the restaurants in terms of food hygiene scores. Problem 2: Graphical presentation The energy contained in each food item is given in the following table. Draw a bar diagram. Fast food items Calories Beef Burger 254 Sausage 290 French Fry 167 Pizza 200 Sandwich 158 Problem 3: Central tendency The amount of calcium carbide in fruit ripening is identified by the food safety authority in the 30 shops. Calcium carbide 45 34 56 45 45 78 51 89 90 110 56 87 98 23 12 76 43 45 65 97 70 25 97 43 27 97 65 45 23 65 1. Measure the third quartile level and first percentile level use of Calcium carbide. 2. Estimate the average use of the Calcium carbide. Problem 4: Correlation and regression A random sample of size 10 has been drawn to check the relationship between the amount of food additive and corresponding prices per unit of frozen food products. Food additive 15 45 34 23 66 34 22 34 56 22 280 178 190 210 150 139 210 180 140 220 Price per unit 1. Draw a scatter plot to find the relationship between food additives and price per unit. 2. Estimate the correlation coefficient between food additives and price per unit. 3. Fit a causal relationship between food additives and price per unit