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Inference on Linear Regression 1. Name___________________________ Is there a linear relationship between the amount of crude oil (in thousands of barrels per day) produced by the U. S. and the amounts of crude oil (in thousands of barrels per day) imported by the U.S. for seven years. ( = 0.05) Produced Imported 5801 11871 5746 11530 5681 12264 5419 13145 5178 13714 5102 13707 5064 13468 2. Is there a linear relationship between the number of initial public offerings of stock issued in a recent 12-year period and the total proceeds of these offerings (in millions of U.S. Dollars). Use a 1% level of significance. # Issues Proceeds 318 34614 486 64927 382 65088 79 34241 70 22136 67 10068 184 32269 168 28593 162 30648 162 35762 21 22762 43 13307 3. Is there a linear relationship between the caloric contents and the sugar contents (in grams) of 11 highfiber breakfast cereals. Calories Sugar 140 6 200 9 160 6 170 9 170 10 190 17 190 13 210 18 190 19 170 10 160 10 4. Use a 90% confidence interval to estimate the average change in test scores for each additional hours spent studying. # hours Test Score 0 40 1 41 2 51 4 48 4 64 5 69 5 73 5 75 6 68 6 93 7 84 7 90 8 95 5. Use a 99% confidence interval to estimate the average change in the number of hours and infant sleeps in a day for each additional year of age for ten infants. Age #Hours 0.1 14.9 0.2 14.5 0.4 13.9 0.7 14.1 0.6 13.9 0.9 13.7 0.1 14.3 0.2 13.9 0.4 14 0.9 14.1 6. The article “Effect of Temperature on the pH of Skim Milk” reported on a study involving x = temperature (ºC) under specified experimental conditions and y = milk pH. Do these data strongly suggest that there is a negative linear relationship between temperature and pH? Use a 0.01 level of significance. x y 4 6.85 4 6.79 24 6.63 24 6.65 25 6.72 38 6.62 38 6.57 40 6.52 45 6.5 50 6.48 55 6.42 56 6.41 60 6.38 67 6.34 70 6.32 78 6.34 7. Construct a 90% prediction interval for shopping center sales when the total square footage of shopping centers. Footage Sales 5 893.8 5.1 933.9 5.2 980 5.3 5.5 5.6 5.7 5.8 5.9 6 6.1 1032.4 1105.3 1181.1 1221.7 1277.2 1339.2 1432.6 1530.4 8. In anthropological studies, an important characteristic of fossils is cranial capacity. Frequently, skulls are at least partially decomposed, so it is necessary to use other characteristics to obtain information about capacity. One such measure that has been used is the length of the lambda-opisthion chord. Suppose that from previous evidence, anthropologists had believed that for each 1-mm increase in chord length, cranial capacity would be expected to increase by 20cm3. Do these new experimental data strongly contradict prior belief? (Use = 0.05) Chord, mm Capacity, cm 78 850 75 775 78 750 81 975 84 915 86 1015 87 1030