Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

\begin{tabular}{|l|c|c|c|}
\hline
& Apples & Oranges & Bananas \\
\hline
Sample 1 & 40 & 64 & 21 \\
\hline
Sample 2 & 43 & 63 & 19 \\
\hline
\end{tabular}

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.

A. About twice as many people prefer apples as prefer bananas.
B. Bananas are preferred much less frequently than apples or oranges.
C. Exactly twice as many people prefer oranges as prefer apples.
D. Exactly three times as many people prefer bananas as prefer oranges.
E. The samples show little variation for each fruit.

Sagot :

GinnyAnswer
Let's analyze the given data and the inferences from the survey step-by-step.

1. Calculate total preferences for each fruit in both samples:
- Total people who prefer apples: [tex]\(40 + 43 = 83\)[/tex]
- Total people who prefer oranges: [tex]\(64 + 63 = 127\)[/tex]
- Total people who prefer bananas: [tex]\(21 + 19 = 40\)[/tex]

2. Inference 1: About twice as many people prefer apples as prefer bananas.
- We compare the number of people who prefer apples to twice the number of people who prefer bananas: [tex]\(83\)[/tex] apples vs [tex]\(2 \times 40 = 80\)[/tex] bananas.
- Since [tex]\(83 \geq 80\)[/tex], this inference is True.

3. Inference 2: Bananas are preferred much less frequently than apples or oranges.
- We compare the preferences:
- Apples: 83
- Oranges: 127
- Bananas: 40
- Bananas are clearly less frequent than both apples and oranges. Thus, this inference is True.

4. Inference 3: Exactly twice as many people prefer oranges as prefer apples.
- We compare the number of people who prefer oranges to twice the number of people who prefer apples: [tex]\(127\)[/tex] oranges vs [tex]\(2 \times 83 = 166\)[/tex] apples.
- Since [tex]\(127 \neq 166\)[/tex], this inference is False.

5. Inference 4: Exactly three times as many people prefer bananas as prefer oranges.
- We compare the number of people who prefer bananas to three times the number of people who prefer oranges: [tex]\(40\)[/tex] bananas vs [tex]\(3 \times 127 = 381\)[/tex] oranges.
- Since [tex]\(40 \neq 381\)[/tex], this inference is False.

6. Inference 5: The samples show little variation for each fruit.
- The variation within each sample can be calculated by finding the difference between the maximum and minimum preferences in each sample.
- For sample 1 (40, 64, 21): Maximum = 64, Minimum = 21, Variation = [tex]\(64 - 21 = 43\)[/tex]
- For sample 2 (43, 63, 19): Maximum = 63, Minimum = 19, Variation = [tex]\(63 - 19 = 44\)[/tex]
- Since the variations are 43 and 44 for samples 1 and 2, respectively, both are greater than 5. Therefore, the samples do not show little variation. This inference is False.

In conclusion, the true inferences based on the data are:
- About twice as many people prefer apples as prefer bananas.
- Bananas are preferred much less frequently than apples or oranges.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.