In this problem, assume that the distribution of differences isapproximately normal. Note: For degrees of freedomd.f. not in the Student's t table, usethe closest d.f. that is smaller. Insome situations, this choice of d.f. may increasethe P-value by a small amount and therefore produce aslightly more \"conservative\" answer.
Is fishing better from a boat or from the shore? Pyramid Lake islocated on the Paiute Indian Reservation in Nevada. Presidents,movie stars, and people who just want to catch fish go to PyramidLake for really large cutthroat trout. Let row B representhours per fish caught fishing from the shore, and let rowA represent hours per fish caught using a boat. Thefollowing data are paired by month from October through April.
| Oct | Nov | Dec | Jan | Feb | March | April |
| B: Shore | 1.7 | 1.9 | 2.0 | 3.2 | 3.9 | 3.6 | 3.3 |
| A: Boat | 1.4 | 1.5 | 1.7 | 2.2 | 3.3 | 3.0 | 3.8 |
Use a 1% level of significance to test if there is a differencein the population mean hours per fish caught using a boat comparedwith fishing from the shore. (Let d = B −A.)
(a) What is the level of significance?
What is the value of the sample test statistic? (Round youranswer to three decimal places.)
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In this problem, assume that the distribution of differences isapproximately normal. Note: For degrees of freedomd.f. not in the Student's t table, usethe closest d.f. that is smaller. Insome situations, this choice of d.f. may increasethe P-value by a small amount and therefore produce aslightly more \"conservative\" answer.
The western United States has a number of four-lane interstatehighways that cut through long tracts of wilderness. To prevent caraccidents with wild animals, the highways are bordered on bothsides with 12-foot-high woven wire fences. Although the fencesprevent accidents, they also disturb the winter migration patternof many animals. To compensate for this disturbance, the highwayshave frequent wilderness underpasses designed for exclusive use bydeer, elk, and other animals. In Colorado, there is a large groupof deer that spend their summer months in a region on one side of ahighway and survive the winter months in a lower region on theother side. To determine if the highway has disturbed deermigration to the winter feeding area, the following data weregathered on a random sample of 10 wilderness districts in thewinter feeding area. Row B represents the average Januarydeer count for a 5-year period before the highway was built, androw A represents the average January deer count for a5-year period after the highway was built. The highway departmentclaims that the January population has not changed. Test this claimagainst the claim that the January population has dropped. Use a 5%level of significance. Units used in the table are hundreds ofdeer. (Let d = B − A.)
| Wilderness District | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| B: Beforehighway | 10.1 | 7.4 | 12.7 | 5.6 | 17.4 | 9.9 | 20.5 | 16.2 | 18.9 | 11.6 |
| A: Afterhighway | 9.1 | 8.2 | 10.0 | 4.1 | 4.0 | 7.1 | 15.2 | 8.3 | 12.2 | 7.3 |
(a) What is the level of significance?
What is the value of the sample test statistic? (Round youranswer to three decimal places.)
