A78 ODD ANSWERS 23. (a) The claim is “the precipitation in Seattle, Washington, was greater than in Birmingham, Alabama.” H0: m1 … m2; Ha: m1 7 m2 (claim) (b) z0 = 1.645; Rejection region: z 7 1.645 (c) 1.019 (d) Fail to reject H0. (e) There is not enough evidence at the 5% level of significance to support the claim that the precipitation in Seattle, Washington, was greater than in Birmingham, Alabama. 25. They are equivalent through algebraic manipulation of the equation. m1 = m2 1m1 - m2 = 0 27. H0: m1 - m2 … 4000; Ha: m1 - m2 7 4000 (claim) Fail to reject H0. There is not enough evidence at the 5% level of significance to support the claim that the difference between the mean annual salaries of entry level software engineers in Santa Clara, California and Greenwich, Connecticut is more than $4000. 29. $1359 6 m1 - m2 6 $13,241 Section 8.2 (page 432) 1. (1) The population standard deviations are unknown. (2) The samples are randomly selected. (3) The samples are independent. (4) The populations are normally distributed or each sample size is at least 30. 3. (a) -t0 = -1.714, t0 = 1.714 (b) -t0 = -1.812, t0 = 1.812 5. (a) t0 = -1.746 (b) t0 = -1.943 7. (a) t0 = 1.729 (b) t0 = 1.895 9. Fail to reject H0. There is not enough evidence at the 1% level of significance to reject the claim. 11. Reject H0. There is enough evidence at the 5% level of significance to reject the claim. 13. (a) The claim is “the mean annual costs of food for dogs and cats are the same.” H0: m1 = m2 (claim); Ha: m1 ≠m2 (b) -t0 = -1.694, t0 = 1.694 Rejection region: t 6 -1.694, t 7 1.694 (c) 2.412 (d) Reject H0. (e) There is enough evidence at the 10% level of significance to reject the pet association’s claim that the mean costs of food for dogs and cats are the same. 15. (a) The claim is “the stomachs of blue crabs from one location contain more fish than the stomachs of blue crabs from another location.” H0: m1 … m2; Ha: m1 7 m2 (claim) (b) t0 = 2.429; Rejection region: t 7 2.429 (c) 1.80 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to support the claim that the stomachs of blue crabs from one location contain more fish than the stomachs of blue crabs from another location. 17. (a) The claim is “the mean household income in a recent year is greater in York County, South Carolina, than it is in Elmore County, Alabama.” H0: m1 … m2; Ha: m1 7 m2 (claim) (b) t0 = 1.734; Rejection region: t 7 1.734 (c) 0.849 (d) Fail to reject H0. (e) There is not enough evidence at the 5% level of significance to support the claim that the mean household income in a recent year is greater in York County, South Carolina, than it is in Elmore County, Alabama. 19. (a) The claim is “an experimental method makes a difference in the tensile strength of steel bars.” H0: m1 = m2; Ha: m1 ≠m2 (claim) (b) -t0 = -2.819, t0 = 2.819 Rejection regions: t 6 -2.819, t 7 2.819 (c) -2.64 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to support the claim that an experimental method makes a difference in the tensile strength of steel bars. 21. (a) The claim is “the new method of teaching reading produces higher reading test scores than the old method.” H0: m1 Ú m2; Ha: m1 6 m2 (claim) (b) t0 = -1.303; Rejection region: t 6 -1.303 (c) -4.286 (d) Reject H0. (e) There is enough evidence at the 10% level of significance to support the claim that the new method of teaching reading produces higher reading test scores than the old method. 23. -11.1 6 m1 - m2 6 12.1 25. -20.8 6 m1 - m2 6 24.8 Section 8.3 (page 442) 1. (1) The samples are randomly selected. (2) The samples are dependent. (3) The populations are normally distributed or the number n of pairs of data is at least 30. 3. Fail to reject H0. There is not enough evidence at the 5% level of significance to support the claim. 5. Reject H0. There is enough evidence at the 10% level of significance to reject the claim. 7. Reject H0. There is enough evidence at the 1% level of significance to reject the claim. 9. (a) The claim is “injections of onabotulinumtoxinA reduce the number of days per month that chronic migraine sufferers have headaches.” H0: md … 0; Ha: md 7 0 (claim) (b) t0 = 2.567; Rejection region: t 7 2.567 (c) d ≈ 13.33; sd ≈ 7.146 (d) 7.914 (e) Reject H0. (f) There is enough evidence at the 1% level of significance to support the claim that injections of onabotulinumtoxinA reduce the number of days per month that chronic migraine sufferers have headaches.
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