Question

practice making inferences based on multiple samples.
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.
the table has two samples (sample 1 and sample 2) with counts for apple, orange, banana: sample 1: apple 40, orange 64, banana 21; sample 2: apple 43, orange 63, banana 19.

Explanation:

Step1: Calculate total for each fruit

Apple: $40 + 43 = 83$
Orange: $64 + 63 = 127$
Banana: $21 + 19 = 40$

Step2: Analyze first statement

Compare apple/banana ratio: $\frac{83}{40} \approx 2.07$, close to 2.

Step3: Analyze second statement

Banana total (40) < Apple (83) and Orange (127).

Step4: Analyze third statement

Orange/apple ratio: $\frac{127}{83} \approx 1.53$, not exactly 2.

Step5: Analyze fourth statement

Banana/orange ratio: $\frac{40}{127} \approx 0.31$, not 3.

Step6: Analyze fifth statement

Check sample variation:
Apple: $|43-40|=3$
Orange: $|63-64|=1$
Banana: $|19-21|=2$
All variations are small.

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.