Question

In the paper titled "Hunters ring dinner bell for ravens. ." (White, 2005), ecologist Crow White asked the question whether ravens actually fly towards (not away from!?) the sound of gunshots, to scavenge the carcass they might find. He went to twelve locations, counted the number of ravens he could see, then shot his gun, waited ten minutes, and counted again. Results are below. Before: 2,1,4,0,1,4,2,0,1,2,4,2 After: 4,0,7,3,3,6,2,1,4,4,7,3 Let uy be the true mean number of ravens before the gunshot, and uy is the true mean number of ravens after the gunshot. We want to test Ho-M1 42 against Hou1 The test statistic is * Enter your answer correct to 2 decimal places. This statistic would come from a t distribution with 11 degrees of freedom distribution if Ho were true. The P-value is Enter your answer correct to 3 decimal places. So we conclude that: There is no evidence against Ho, that is, there is no evidence that there are more ravens after gunshots. There is strong evidence for Ho, that is, there is strong evidence that there is no difference in ravens before and after gunshots. There is no evidence for Ho, that is, there is no evidence that there is no difference in ravens before and after gunshots. There is strong evidence against Ho, that is, there is strong evidence that there are more ravens after gunshots.

Answer 1

The following table is obtained: Sample 1 Sample 2 Difference = Sample 1 - Sample 2 2 4 -2 1 0 1 4 7 0 3 -3 1 3 -2 4 6 -2 2 2 0 0 1 -1 1 4 -3 2 4 -2 4 7 -3 2 3 -1 Average 1.917 3.667 -1.75 St. Dev. 1.443 2.188 1.288 n 12 12 12

From the sample data, it is found that the corresponding sample means are: X1 = 1.917 X2 = 3.667 Also, the provided sample standard deviations are: 81 = 1.443 82 = 2.188 and the sample size is n = 12. For the score differences we have D = -1.75 SD = 1.288 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: up = 0 Ha: up < 0 This corresponds to a left-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the degrees of freedom are df = 11. Hence, it is found that the critical value for this left-tailed test is te = -1.796, for a= 0.05 and df = 11. The rejection region for this left-tailed test is R= {t:t< -1.796} (3) Test Statistics The t-statistic is computed as shown in the following formula: D -1.75 1.288/V12 -4.706 SD/n (4) Decision about the null hypothesis Since it is observed that t = -4.706 <tc = -1.796, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p= 0.0003, and since p= 0.0003 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion : There is strong evidence against H0, there is strong evidence that there are more ravens after gunshot