Question

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom dl. not in the Student's t table, use the dosest d.. that is smaller, In some situations, this choice of d.l. may increase the P-value by a small amount and therefore produce a slightly more "conservative answer. Is fishing better from a boat or from the shore? Pyramid Lake is located on the Palute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let row represent hours per fish caught fishing from the shore, and let row A represent hours per fish caught using a boat. The following data are paired by month from October through April. Oct Nov Dec Jan Feb March April 8: Shore 1.5 1.8 2.0 3.9 3.6 3.3 A: Boat 1.3 1.6 2.2 3.3 3.0 3.8 Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore. (Let d - 8 - A.) (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? Ho Hd = 0; H: Hd < 0; left-tailed Ho Ho + 0; H: H = 0; two-tailed Ho: H0; H: 0; two-tailed O Ho: M - 0; H:He > 0; right-tailed (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that has an approximately uniform distribution. The standard normal. We assume that has an approximately normal distribution The Student's t. We assume that d has an approximately uniform distribution. The Student's t. We assume that has an approximately normal distribution What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the p-value

Answer 1

Sol: B А el B-A 1.5 to y 0.1 1.8 1.3 0.5 1.6 Oot 2.0 3.2 3.9 3.6 2.2 3.3 0.6 3.3 3-0 3.8 0.6 -0.5 Meanld)= 0.3858 Edi Stnd.devesu- VH 2(dj-51 to zdi-))} = 0.4741 ca) L=0.01 Level of =0. Level of significance Null and Alternative hypoltesis ll=0; Hall to (two tailed test) (b) option(D) is correct. Test Statistic che dolly 8.153 Salin 8.4741 Ho: el 0.3858 C) P-value At df=n-1= 7-1=6, t=2.153 p-value =0.0748 P-value > 2 Level of s Stg(0.01) So, Fail to Reject Ho.