A food-protection agency counts the number of insect heads found per 100-gram batch of wheat flour. The researchers have 500 batches, and they want to know whether the frequency of insect heads in batches follows a distribution called a Poisson distribution. To generate the expected frequencies of batches with different numbers of insect heads under a Poisson distribution, they had to estimate the mean number of insect heads per batch from the data. The 500 batches included at least 5 batches having 0, 1, 2, 3, or 4 insect heads. No batches had more than four heads. Given this information, there areclasses (k).

The correct answer is k = 5.

Step-by-step explanation:

The Chi-square goodness of fit test would be used to determine whether the frequency of insect heads in batches follows a distribution called a Poisson distribution.

The hypothesis for the test can be defined as follows:

H₀: The frequency of insect heads in batches does not follows a Poisson distribution.

Hₐ: The frequency of insect heads in batches follows a Poisson distribution.

Assume that the significance level of the test is, α = 0.05.

The Chi-square test statistic is given by:

It is provided that the 500 batches included at least 5 batches having 0, 1, 2, 3, or 4 insect heads. No batches had more than four heads.

So, the number of classes or categories are, k = 5.

Thus, the correct answer is k = 5.

h is the x-coordinate of the vertex

step-by-step explanation:

we have

in this function

the point represent the vertex of the function

so

h is the x-coordinate of the vertex

k is the y-coordinate of the vertex