Please show all work thank you Problem 6 An ecological resea

Please show all work, thank you!

Problem 6. An ecological researcher studied the interation between birds of two subspecies, the Carolina Junco and the Northern Junco. He placed a Carolina male and a Northern male, matched by size, together in an aviary and observed their behavior for 45 minutes beginning at dawn. This was repeated on different days with different pairs of birds. The table shows counts of the episodes n which one bird displayed dominance over the other. (a) Use a sign test to compare the subspecies. Use a non-directional alternative and let alpha = 0.01. (b) Use a Wilcoxon signed-rank test to compare the subspecies, use a non-directional alternative and let alpha = 0.01.

Solution

(a)

Following table shows thesign for differences:

H0: The median value of the distribution is m , values larger (+) and smaller (-) than the median are same.

Ha: The median value of the distribution is m , values larger (+) and smaller (-) than the median are not same.

Since n is 8 so it is less than 25. Therefore test statistics will be number of signs which are less. that is test statistics will be x=0 . P-value of the test is 0.00781. Since p-value is less than 0.01 so we reject the null hypothesis.

(b)

Following table shows the Wilcoxon signed-rank test:

Sum of positive ranks is 0 and sum of negative ranks is -36. So W=0 for N=8. Since critical value of the test for level of significance 0.01 is 2 so we reject the null hypothesis.

Pair	Northern Was Dominant	Carolina Was Dominant	Sign (Northern-Carolina)
1	0	9	(-)
2	0	6	(-)
3	0	22	(-)
4	2	16	(-)
5	0	17	(-)
6	2	33	(-)
7	1	24	(-)
8	0	40	(-)