Question

Two insecticides will be compared for their effectiveness in eliminating aphids on tomato plants. Forty tomato plants of the Big Boy variety will be randomly allocated to two groups of twenty each. The first group of 20 plants will be sprayed with insecticide A and the other group of 20 plants with insecticide B. After two weeks, the number of aphids on each plant will be counted. A test will be performed to determine whether the mean number of aphids differs significantly for the two insecticides.

What procedure should she use to compare the mean number of aphids found on the two groups of plants?

Answer 1

The student should use a two-sample t-test to compare the mean number of aphids on the tomato plants treated with insecticide A and B. If the data does not meet the assumptions of the t-test, a non-parametric test like the Mann-Whitney U test can be used instead.

Step-by-step explanation:

To compare the mean number of aphids found on the two groups of tomato plants after treatment with different insecticides, the student should use a statistical test. A suitable procedure for this comparison is the two-sample t-test, which will determine if there is a statistically significant difference in the mean number of aphids between the two groups. This test assumes that the data are normally distributed; however, if the normality assumption does not hold, a non-parametric alternative such as the Mann-Whitney U test may be used.

The setup involves treating one group of plants with insecticide A and another with insecticide B. After applying the treatments, the student will count the aphids on each plant in both groups. The mean number of aphids in each group will be calculated and compared using the chosen statistical test.

Before conducting the t-test, it is essential to check for the assumptions of normality and equal variances. If these assumptions are met, the two-sample t-test can provide insight into whether the effectiveness of the insecticides is significantly different or not. The conclusion from this test will enable the student to determine which insecticide is more effective at eliminating aphids from tomato plants.

Answer 2

The t-test

Step-by-step explanation:

The researcher should use a t-test to compare the two means and check if they are significantly different from each other.

In using the t-test, both null (H0) and alternate (H1) hypothesis are made such that:

• H0: n1 = n2
• H1: n1≠ n2

Thereafter, the value of t is calculated and compared to its critical value on the table. The formula for calculating the t goes thus:

`t = \frac{Y_1 - Y_2}{\sqrt{(S_1)/(n_1) + (S_2)/(n_2) } }`

where, Y1 = mean of population 1, Y2 = mean of population 2, S1 = variance of population 1, S2 = variance of population 2, n1 = number of individuals in population 1 and s2 = number of individuals in population 2.

At the end of the day, if the calculated t value is more than the critical value of t, the H0 is rejected and it shows that the two means are significantly different. Otherwise, the H0 is accepted and this shows that there is not significant difference between the mean of population 1 and that of 2.