statics questions

1. The heights (in feet) for a random sample of world-famous cathedrals are listed. In addition, the heights for a random sample of the tallest buildings in the world are listed. Is there sufficient evidence at a = 0.05 to conclude that there is a difference in the variances in height between the two groups? Cathedrals 72 114 157 56 83 108 90 151 Tallest Buildings 452 442 415 391 355 344 310 302 209 2. At a large department store, customers were asked to rate the service and the materials purchased on a scale from 1 to 10, with 10 being the highest rating. Then the amount that they spent was recorded. Is there evidence of a relationship between the rating and the amount that they spent? Use a = 0.01. Start by creating a scatter plot. Only do a regression analysis if there is a linear relationship. Rating (x) 6 8 2 9 1 5 Amount Spent (y) $90 $83 $42 $110 $27 $31 3. A researcher desires to know whether if the speed of parts being made by an operator on a machine (in parts per hour) is related to the time (in hours) it takes for the operator to learn to use a new machine. The data are shown. Use a = 0.01. Speed (x) 48 74 52 79 83 56 85 63 88 74 90 92 Time (y) 7 8 3.5 2 6 2.3 58 2.1 4.5 1.9 1.5 If there is a significant relationship, predict the time it will take an average operator who can produce 72 parts per hour to learn the new machine. 4. Given the following pairs of data, determine the correlation coefficientr and determine if there is a strong linear correlation. Also, determine the regression equationy' = a + bx. Determine y' for x = 3 and x = 7. Use a = 0.05. (2,9) (4,6) (6,3) (8,1)