A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyla, and he believes the phyla should be uniformly distributed. A simple random sample of 60 alga was obtained, and each was categorized as being a member of Rhodophyta, Chlorophyta, or Heterokontophyta. The observed counts were 25, 25, and 10, respectively. What is the chi-square statistic for the phycologist's test?

Question

Quizplus · Accepted Answer

The null hypothesis is that the proportion of algae samples from each phyla is uniformly distributed. This means that we expect 20 out of the 60 samples to be from each phylum.

To find the chi-square statistic, we use the formula:

chi-square = Σ(observed - expected)^2 / expected

For the Rhodophyta category:

(observed - expected)^2 / expected = (25 - 20)^2 / 20 = 1.25

For the Chlorophyta category:

(observed - expected)^2 / expected = (25 - 20)^2 / 20 = 1.25

For the Heterokontophyta category:

(observed - expected)^2 / expected = (10 - 20)^2 / 20 = 5

Adding up these three values, we get:

chi-square = 1.25 + 1.25 + 5 = 7.50

Therefore, the chi-square statistic for the phycologist's test is 7.50, which corresponds to choice B.

A Phycologist Is Interested in Determining the Proportion of Algae