Question

a two - way table shows how many students in each grade prefer salty or sweet snacks. explain how you could use the table to determine whether there is an association between grade level and snack preference.
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Explanation:

Step1: Calculate the relative frequencies

For each grade level, calculate the relative frequency of preferring salty snacks and sweet snacks. For 6th grade, relative frequency of salty snacks is $\frac{18}{30}=0.6$, and for sweet snacks is $\frac{12}{30} = 0.4$. For 7th grade, relative frequency of salty snacks is $\frac{10}{30}\approx0.33$, and for sweet snacks is $\frac{20}{30}\approx0.67$. For 8th grade, relative frequency of salty snacks is $\frac{14}{30}\approx0.47$, and for sweet snacks is $\frac{16}{30}\approx0.53$.

Step2: Compare the relative frequencies

If the relative frequencies of snack preference (salty vs sweet) are different across grade levels, then there is an association. Here, in 6th grade, salty snacks are more preferred ($0.6$ vs $0.4$ for sweet). In 7th grade, sweet snacks are more preferred ($0.67$ vs $0.33$ for salty). In 8th grade, sweet snacks are slightly more preferred ($0.53$ vs $0.47$ for salty). Since the relative frequencies vary by grade level, there is an association.

Answer:

By calculating the relative frequencies of snack preference (salty or sweet) for each grade level (e.g., for 6th grade: $\frac{18}{30}=0.6$ for salty, $\frac{12}{30}=0.4$ for sweet; 7th grade: $\frac{10}{30}\approx0.33$ for salty, $\frac{20}{30}\approx0.67$ for sweet; 8th grade: $\frac{14}{30}\approx0.47$ for salty, $\frac{16}{30}\approx0.53$ for sweet) and comparing them. Since the relative frequencies of snack preference differ among grade levels (6th - more salty, 7th - more sweet, 8th - slightly more sweet), there is an association between grade level and snack preference.