Please show all work thank you In a study of preening behavi

Please show all work, thank you!

In a study of preening behavior in the fruitfly Drosphila melanogaster, a single experimental fly was observed for three minutes while in a chamber with 10 other flies of the same sex. The observer recordeded the timing of each episode (bout) of preening by the experimental fly. This experiment was replicated 15 times with male flies and 15 times with female flies (different flies each time). One question of interest was whether there is a sex difference in preening behavior. The observed preening times (average time per bout, in seconds) were as follows. Let males be Sample 1, and females by Sample 2. For this data, x1 = 2.127, s1 = 0.5936, x2 = 4.093, s2 = 3.014. (a) Use a Wilcoxon-Mann-Whitney test to investigate whether or not there is a difference in preening behavior between male and female flies. Let alpha = 0.01. (b) Conduct a 2 sample t test to investigate whether or not there is a difference in preening behavior between male and female flies. Let alpha = 0.01.

Solution

(a)

Performing Mann Whitney Utest in MS-EXCEL using the real statistics add-in we get the following results.

Since U value is less than U-critical there must not be any difference in the preening test between male and female flies.

(b)

T-test gives the following results

Since we are checking only equality or not, we will only use the results of two tail tests.

P-value is more than 0.01, hence we accept the hypothesis that there is no difference in the preening behaviour between male and female flies.

Mann-Whitney Test for Two Independent Samples
	Male	Female
count	15	15
median	2.2	2.8
rank sum	155.5	309.5
U	189.5	35.5
	one tail	two tail
alpha	0.01
U	35.5
mean	112.5
std dev	24.10913
z-score	3.173072
effect r	0.579321
U-crit	55.91378	49.899
p-value	0.000754	0.001508
sig (norm)	yes	yes
U-crit	56	51
sig (table)	yes	yes