Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
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.
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.
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
