General Direction: Write all your answers in separate sheet of paper. 1. A business professor studied students' performance in their comprehension test at the first year level. The norm for the population mean is designed to yield a scaled score value of 50 for the first-year students. A random of 10 students with scores are the following: 48, 42, 55, 35, 50, 47, 45, 45, 39 and 42. Could this sample be representative of the population for whom the test is designed? Test the hypothesis at 0.05 level. 2. From a business class of 16 equally capable students using programmed materials, 5 are selected at random and given additional instruction by the professor. The results of the final examination were as follows: Students Grouping Grades Additional instruction 87, 79, 78, 91, 80, 82, 84, 79, 85 No additional instruction 75, 80, 64, 82, 83, 79, 67 Test with alpha = 0.05 to determine if additional instruction affects the average grade. 3. It is claimed that a new diet will reduce a person's weight, on the average in a period of two weeks. The weight of 10 women who followed this diet were recorded before and after a 2-week period, yielding the following data: Woman 2 3 4 5 6 7 8 9 10 Weight before 58.5 60.3 61.7 69.0 64.2 62.6 56.7 63.6 68.2 59.4 Weight after 60.0 54.9 58.1 62.1 58.5 59.9 54.4 60.2 62.3 58.7 Test the hypothesis that the diet reduces the weight against the alternative hypothesis that there is a significant difference. 4. The following data represent the operating times in hours for three types of scientific pocket calculators before recharge is required Calculator A 4.9 6.1 4.3 4.6 5.3 Calculator B 5.5 5.4 6.2 5.8 5.5 5.2 4.8 Calculator C 6.4 6.8 5.6 6.5 6.3 6.6 Use a 0.05 level of significance, to test the hypothesis that the operating times for all three calculators are equal