Question

A gardener wants to know if soaking seeds in water before planting them increases the proportion of seeds that germinate. To investigate, the gardener will assign 50 seeds to be soaked before planting and 50 seeds to be planted without being soaked. After two weeks, the gardener will record how many seeds in each group germinated and construct a 95 percent confidence interval for the difference in proportions. Which of the following conditions for inference should be met?

a. The seeds should be randomly assigned to a treatment.
b. The group sizes should be less than 10 percent of the population sizes.
c. The number of successful seeds and unsuccessful seeds in each group should be at least 10.

Answer 1

The condition for inference that should be met is (c) The number of successful seeds and unsuccessful seeds in each group should be at least 10. This condition is related to the assumption of the normal approximation to the sampling distribution of the difference in proportions.

In order to construct a confidence interval for the difference in proportions between the two groups, we need to assume that the difference in proportions follows an approximately normal distribution. This assumption holds if the number of successful and unsuccessful seeds in each group is at least 10. If this condition is not met, the normal approximation may not be valid, and other methods may need to be used to construct a confidence interval.

Condition (a) The seeds should be randomly assigned to a treatment, is important for minimizing bias in the assignment of seeds to the treatment and control groups, but it is not directly related to the conditions for inference.

Condition (b) The group sizes should be less than 10 percent of the population sizes, is related to the assumption of independence between the two groups, but it is not directly related to the conditions for inference.