Question

the box plots show the heights of sunflower plants in a random sample of 40 plants from field a and a random sample of 40 plants from field b. why can you use the box plots to make inferences about plant heights at the two sunflower fields? the data include all of the plants at each of the sunflower fields. the samples of 40 sunflower plants are both taken from the same population. the random samples are likely to be representative of the population of sunflower plants at each field.

Explanation:

When making inferences about a population (the sunflower plants in each field), random samples are used. Random sampling helps to reduce bias. If a sample is random, it is more likely to mirror the characteristics of the entire population. Box - plots are constructed from these samples. If the samples are random and of a reasonable size (here \(n = 40\) for each field), we can use the box - plots (which show measures like median, quartiles, range etc.) to make inferences about the population (the sunflower plants in each field).
The first option is incorrect because the data is from samples (40 plants) not all plants in the fields. The second option is incorrect because Field A and Field B are two different populations (different fields).

Answer:

The random samples are likely to be representative of the population of sunflower plants at each field.