Question

the two - way table of row relative frequencies below shows data on nationality and eye color.

based on the data, which of the following statements must be true?

choose 1 answer:

a there are the same number of english people and italian people with other eye colors.

b italians are more likely to have brown or hazel eyes than germans are.

c a german person is more likely to have brown or hazel eyes than to have blue or green eyes.

d a person with brown or hazel eyes is least likely to be german.

Explanation:

• Option A: The row - relative frequencies for "Other" eye colors are \(0.02\) for English and \(0.02\) for Italian. But these are relative frequencies. The actual number of people depends on the total number of English and Italian people (which is unknown). So, we can't say the number of people is the same.
• Option B: The row - relative frequency of brown or hazel eyes for Italians is \(0.80\) and for Germans is \(0.47\). Since \(0.80>0.47\), Italians are more likely to have brown or hazel eyes than Germans.
• Option C: For Germans, the row - relative frequency of brown or hazel eyes is \(0.47\) and for blue or green eyes is \(0.52\). Since \(0.47 < 0.52\), a German is less likely to have brown or hazel eyes than blue or green eyes.
• Option D: We don't have information about the column - relative frequencies (the proportion of people with brown or hazel eyes who are German, English, or Italian). We only have row - relative frequencies (the proportion of English, German, or Italian people with a certain eye - color).

Answer:

B. Italians are more likely to have brown or hazel eyes than Germans are.