Question

a survey was conducted asking people about their favorite fruit. which inferences about the population are true based on the data? check all that apply.
□ about twice as many people prefer apples as prefer bananas.
□ bananas are preferred much less frequently than apples or oranges.
□ exactly twice as many people prefer oranges as prefer apples.
□ exactly three times as many people prefer bananas as prefer oranges.
□ the samples show little variation for each fruit.

Explanation:

Step1: Analyze preference ratio of apples and bananas

For Sample 1: $\frac{40}{21}\approx1.9$, for Sample 2: $\frac{43}{19}\approx2.26$. So about twice as many people prefer apples as prefer bananas.

Step2: Compare preferences of fruits

In both samples, the number of people who prefer bananas (21 and 19) is much less than those who prefer apples (40 and 43) or oranges (64 and 83).

Step3: Check ratio of oranges and apples

For Sample 1: $\frac{64}{40} = 1.6$, for Sample 2: $\frac{83}{43}\approx1.93$. Not exactly twice.

Step4: Check ratio of bananas and oranges

For Sample 1: $\frac{21}{64}\approx0.33$, for Sample 2: $\frac{19}{83}\approx0.23$. Not exactly one - third.

Step5: Analyze sample variation

For apples: $|43 - 40|=3$, for oranges: $|83 - 64| = 19$, for bananas: $|21 - 19|=2$. The samples show some variation for oranges.

Answer:

• About twice as many people prefer apples as prefer bananas.
• Bananas are preferred much less frequently than apples or oranges.
• The samples show little variation for each fruit.