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?

The t-test

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:

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

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.