Question

q show what you know! based on the data in the table, which of the following is the best conclusion? there is no association between pet type and flavor preference. dog owners are more likely to prefer chocolate, while cat owners are more likely to prefer vanilla. the majority of students prefer chocolate. cat owners are more likely to prefer chocolate.

Explanation:

Step1: Calculate the proportion of cat owners who prefer chocolate

The number of cat owners who prefer chocolate is \(9\), and the total number of cat owners is \(30\). The proportion is \(\frac{9}{30}=\frac{3}{10} = 0.3\).

Step2: Calculate the proportion of cat owners who prefer vanilla

The number of cat owners who prefer vanilla is \(21\), and the total number of cat owners is \(30\). The proportion is \(\frac{21}{30}=\frac{7}{10}=0.7\).

Step3: Calculate the proportion of dog owners who prefer chocolate

The number of dog owners who prefer chocolate is \(18\), and the total number of dog owners is \(30\). The proportion is \(\frac{18}{30}=\frac{3}{5} = 0.6\).

Step4: Calculate the proportion of dog owners who prefer vanilla

The number of dog owners who prefer vanilla is \(12\), and the total number of dog owners is \(30\). The proportion is \(\frac{12}{30}=\frac{2}{5}=0.4\).

Step5: Analyze each option

• Option 1: There is no association between pet type and flavor preference

Since the proportions of flavor preferences are different for cat and dog owners (\(0.3
eq0.6\) for chocolate and \(0.7
eq0.4\) for vanilla), there is an association. So this option is wrong.

• Option 2: Dog owners are more likely to prefer chocolate, while cat owners are more likely to prefer vanilla

As calculated above, for dog owners \(\frac{18}{30}=0.6\) prefer chocolate and for cat owners \(\frac{21}{30} = 0.7\) prefer vanilla. This option is correct.

• Option 3: The majority of students prefer chocolate

The total number of students who prefer chocolate is \(9 + 18=27\), and the total number of students is \(60\). \(\frac{27}{60}=0.45<0.5\), so the majority do not prefer chocolate. This option is wrong.

• Option 4: Cat owners are more likely to prefer chocolate

As calculated \(\frac{9}{30}=0.3\) (cat - chocolate) and \(\frac{21}{30}=0.7\) (cat - vanilla). So cat owners are more likely to prefer vanilla. This option is wrong.

Answer:

Dog owners are more likely to prefer chocolate, while cat owners are more likely to prefer vanilla.