To determine the meaning of the 0.3 in the highlighted cell of the relative frequency table, we can analyze the given table. The table summarizes the relative frequencies of different combinations of chili and cheese on hot dogs as ordered by customers.
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & Cheese & No cheese & Total \\
\hline Chili & 0.1 & 0.3 & 0.4 \\
\hline No chili & 0.2 & 0.4 & 0.6 \\
\hline Total & 0.3 & 0.7 & 1.0 \\
\hline
\end{tabular}
\][/tex]
First, let’s define what each column represents:
- The "Cheese" column shows the relative frequency of customers who ordered hot dogs with cheese.
- The "No cheese" column shows the relative frequency of customers who ordered hot dogs without cheese.
- The "Total" column shows the total relative frequency of customers who ordered hot dogs with or without chili, regardless of cheese.
We are specifically looking at the 0.3 in the "No cheese" column for the row labeled "Chili."
To interpret this value, it indicates the proportion (relative frequency) of customers who ordered hot dogs with chili but without cheese. Let's examine each option:
A. 30% of his customers ordered chili but no cheese on their hot dog.
- This statement relates directly to the "No cheese" column for "Chili" row, which reflects 0.3 (or 30%).
B. 30% of his customers ordered chili on their hot dog.
- This statement refers to the total frequency of customers who ordered chili, which is given in the "Total" column for the "Chili" row: 0.4 (or 40%).
C. 30% of his customers ordered no cheese on their hot dog.
- This statement concerns the total frequency in the "No cheese" column, which sums the frequencies of both "Chili" and "No chili" rows for "No cheese": 0.3 + 0.4 = 0.7 (or 70%).
D. 30% of the customers that ordered chili ordered no cheese.
- This statement would refer to a conditional probability calculated as the ratio of customers who ordered chili but no cheese to those who ordered chili, which is 0.3 / 0.4 (or 75%).
Given these interpretations, the correct meaning of the 0.3 in the highlighted cell is:
30% of his customers ordered no cheese on their hot dog.
Thus, the correct answer is:
C. [tex]$30 \%$[/tex] of his customers ordered no cheese on their hot dog.
