Tests of Significance and Confidence Intervals for Means 6. The quantity of dissolved oxygen is a measure of water pollution. Water samples were taken at four different locations in a river in an effort to determine if water pollution varied from location to location. Riverbank 1 was 500m above an industrial plant water discharge and near the shore. Midstream 1 was 200m above the plant and in midstream. Riverbank 2 was 50m downstream from the plant and near the shore. Midstream 2 was 200m downstream from the plant and in midstream. Use a 5% significance level to test the claim that the quantity of dissolved oxygen does not vary from one location to another. Assume that the population distributions are normal. Riverbank 1 Riverbank 2 Midstream 1 Midstream 2 7.3 4.2 6.6 4.4 5.9 5.9 7.1 5.1 7.7 4.9 7.7 6.2 6.8 5.1 8.0 7.1 6.2 4.5 7. A study was conducted to see if an herbal supplement helped to reduce weight. After 12 weeks, 42 subjects using the herbal supplement and a high-fiber, low calorie diet had a mean weight loss of 4.1 pounds and a standard deviation of 3.9 pounds. During the same period, 42 subjects using a placebo and a high-fiber, low calorie diet had a mean weight loss of 3.2 pounds with a standard deviation of 1.3 pounds. a. Construct a 95% confidence interval for the difference of the two population means. b. Do the data from the study indicate that the herbal supplement is effective in helping to reduce weight? 8. As part of their training, police cadets took a special course on identification awareness. To determine how the course affects a cadet's ability to identify a suspect, the 15 cadets were first given an identification awareness exam and then, after, the course were tested again. The police school would like to use these results to see if the identification awareness course changes a cadet's score. Assume the underlying distributions are normal. What conclusion would you draw at the 5% significance level? Cadet 1 2 3 4 5 6 8 - 9 10 11 12 13 14 15 Post 93 70 81 79 54 94 91 77 65 95 89 78 80 - 76 Pre 76 72 75 68 65 54 88 81 65 57 86 87 78 77 76 9. The prices (in dollars) for 16 randomly selected automobile batteries are shown in the table. The prices are classified according to battery type. At the 5% significance level, is there enough evidence to conclude that the means are different? Assume that each population of battery types is normally distributed. Type A 89 84 74 90 70 60 Type B 83 63 65 63 85 65 Type C 65 75 64 50