Question

Problem 3:

In a study to determine the effectiveness of a synthetically produced mate attractant chemical (pheromone), the synthetic hormone was compared with a natural male pheromone for its ability to attract female fruit fly. Fifteen synthetic baits and 14 natural baits were placed at random in a group of peach trees and the number of female fruit fly attracted to the baits over a 2 hour period were counted (data shown below).

Is there a difference in the attractiveness of the synthetic and natural pheromones?

Synthetic: 5, 7, 11, 13, 25, 35, 22, 17, 9, 20, 18, 31, 12, 16, 10

Natural: 6, 47, 41, 19, 21, 14, 8, 23, 32, 28, 29, 24, 15, 27

Answer 1

The data is as follows:

Synthetic	Natural
5	6
7	47
11	41
13	19
25	21
35	14
22	8
17	23
9	32
20	28
18	29
31	24
12	15
16	27
10

Let's see the descriptive statistics of both the variables:

	Synthetic	Natural
Mean	16.73333333	23.85714286
Variance	75.20952381	132.9010989

To check the difference in the attractiveness of the synthetic and natural pheromones, we will run a two sample t-test assuming equal variances (one sample variance is no larger than twice the other)

Let's run the two-sample t-test:

To calculate Sp (Pooled variance):

Pooled variance = 102.98

n1 = 15, n2 = 14

t-statistic = -1.89

The t-critical value at df = 15 + 14 - 2 = 27 and 0.05 significance level is +-2.05

As t-calculated = -1.89 is not less than -2.05, we cannot reject the null hypothesis. The p-value = 0.069

Therefore, we can conclude that there is no difference in the attractiveness in the baits