Q. 72 - The Practice of Statistics for AP

Question

Velvetleaf is a particularly annoying weed in cornfields. It produces lots of seeds, and the seeds wait in the soil for years until conditions are right for sprouting. How many seeds do velvetleaf plants produce? The Fathom histogram below shows the counts from $28$ plants that came up in a cornfield when no herbicide was used. Explain why it would not be wise to use a one-sample $t$ interval to estimate the mean number of seeds $\mu$ produced by velvetleaf plants.

Step-by-Step Solution

Answer

The NORMAL requirement to use the $t$-procedure is thus not satisfied.

Step 1: Given Information

Step 2: Explanation

In the histogram, we note that there are $2$ outliers (to the right) and the distribution appears to be left-skewed (since the outliers are to the right).

Since the distribution contains outliers and skewness, the distribution is NOT approximately a normal distribution.