840 CHAPTER 12 Statistics 12.6 29. Hiking The following table shows the number of hiking permits issued for a specific trail at Yellowstone National Park for selected years and the corresponding number of bears sighted by the hikers on that trail. Hiking permits 765 926 1145 842 1485 1702 Bears 119 127 150 119 153 156 a) Construct a scatter diagram with hiking permits on the horizontal axis. * b) Use the scatter diagram in part (a) to determine whether you believe that a correlation exists between the number of hiking permits issued and the number of bears sighted by hikers. If so, is it a positive or negative correlation? Yes; positive c) Calculate the correlation coefficient between the number of hiking permits issued and the number of bears sighted by hikers. 0.925 d) Determine whether a correlation exists at 0.05. α= Yes e) Determine the equation of the line of best fit between the number of hiking permits issued and the number of bears sighted by hikers. Round both m and b to the nearest hundredth. y x 0.04 88.17 = + f) Assuming that this trend continues, use the equation of the line of best fit to estimate the number of bears sighted if 1500 hiking permits were issued. ≈148 bears 30. Daily Sales For six weeks, Ace Hardware recorded the price of a particular item and the corresponding sales of that item as shown in the table below. Price ($) 0.75 1.00 1.25 1.50 1.75 2.00 Number sold 200 160 140 120 110 95 a) Construct a scatter diagram with price on the horizontal axis. * b) Use the scatter diagram in part (a) to determine whether you believe that a correlation exists between the price of the item and number sold. If so, is it a positive or a negative correlation? Yes; negative c) Determine the correlation coefficient between the weekly price and the number of items sold. 0.973 − d) Determine whether a correlation exists at 0.05. α= Yes e) Determine the equation of the line of best fit for the price and the number of items sold. y x 79.4 246.7 = − + f) Use the equation in part (e) to estimate the number of items sold if the price is $1.60. ≈120 sold $ 12.3–12.5 Men’s Weight In Exercises 31–38, use the data below which was obtained from a study of the weights of adult men. Mean 192 lb First quartile 178 lb Median 185 lb Third quartile 232 lb Mode 180 lb 86th percentile 239 lb Standard deviation 23 lb 31. What is the most common weight? 180 lb 32. What weight did half of those surveyed exceed? 185 lb 33. About what percent of those surveyed weighed more than 232 lb? 25% 34. About what percent of those surveyed weighed less than 178 lb? 25% 35. About what percent of those surveyed weighed more than 239 lb? 14% 36. If 100 men were surveyed, what is the total weight of all the men? 19,200 lb 37. What weight represents two standard deviations above the mean? 238 lb 38. What weight represents 1.8 standard deviations below the mean? 150.6 lb 12.2–12.5 For Exercises 39–50, use the following data, which show the number of children per family for 20 families. 0312140076 2222330101 In Exercises 39– 44, determine the following. 39. Mean 2 40. Mode 0 and 2 41. Median 2 42. Midrange 3.5 43. Range 7 44. Standard deviation 3.79 1.95 ≈ 45. Construct a frequency distribution. * *See Instructor Answer Appendix
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