Question

Use sign test for the population median to solve this question. In a laboratory experiment, insects of a certain type are released in the middle of a circle drawn on plain, flat table. A scent, intended to attract that type of insect, located at one end of the table. Each insect is released singly and is observed until it crosses the boundary of the circle. At the conclusion of the experiment it was found that 33 insects crossed the boundary "away" from the scent; and 12 did not cross the boundary. Is there sufficient evidence to indicate that the scent attracts this type of insect? (α = .05)

Answer 1

Here, no. of insects crossed the boundary away from the scent = negatives = 33.
no. of insects not crossing the boundary = positives = 12.
n = sample size = 12 + 33 = 45.

Here, the test statistic (X) calculates the no. of positives and, under H0, follows a Binomial distribution with n = 45 and p = 0.5.
Hence, p-value = P(X <= 12) = 0.0012.

Since p-value < 0.05, we reject H0 and conclude that there is a significant difference. Hence, there is not enough evidence to indicate that the scent attracts this type of insect.