Question
Pick up Browse Total
Weekday 25 12 37
Weekend 17 45 62
Total 42 57 99
Sal kept track of how many people visited the local library and recorded their purpose for visiting. Using marginal relative frequency, what interpretation can you make from the data in the two-way table?
(1 point)
Responses
A high percentage of people pick up on the weekend.
A high percentage of people pick up on the weekend.
People only come to pick up reserved books during the week.
People only come to pick up reserved books during the week.
The pick-up service is not very popular at this library.
The pick-up service is not very popular at this library.
The weekend is the most popular time to visit.
Answers
GPT-4o mini
To analyze the data in the two-way table using marginal relative frequency, we can calculate the proportions of each category relative to the total.
1. **Total Visits**: 99
2. **Percentage of Visits by Purpose**:
- Pick up: \( \frac{42}{99} \approx 0.4242 \) or 42.42%
- Browse: \( \frac{57}{99} \approx 0.5758 \) or 57.58%
3. **Percentage of Visits by Time**:
- Weekday: \( \frac{37}{99} \approx 0.3737 \) or 37.37%
- Weekend: \( \frac{62}{99} \approx 0.6263 \) or 62.63%
Now, let's interpret the options:
- **A high percentage of people pick up on the weekend.** This is misleading as the overall percentage of people picking up is around 42.42% regardless of the day.
- **People only come to pick up reserved books during the week.** This is not supported by the data as there are visitors on the weekend as well.
- **The pick-up service is not very popular at this library.** This interpretation is valid as only about 42.42% of the total visits were for picking up.
- **The weekend is the most popular time to visit.** This is true since approximately 62.63% of the visits occurred on the weekend.
Given these analyses, the most accurate interpretation based on marginal relative frequency is **"The weekend is the most popular time to visit."**
1. **Total Visits**: 99
2. **Percentage of Visits by Purpose**:
- Pick up: \( \frac{42}{99} \approx 0.4242 \) or 42.42%
- Browse: \( \frac{57}{99} \approx 0.5758 \) or 57.58%
3. **Percentage of Visits by Time**:
- Weekday: \( \frac{37}{99} \approx 0.3737 \) or 37.37%
- Weekend: \( \frac{62}{99} \approx 0.6263 \) or 62.63%
Now, let's interpret the options:
- **A high percentage of people pick up on the weekend.** This is misleading as the overall percentage of people picking up is around 42.42% regardless of the day.
- **People only come to pick up reserved books during the week.** This is not supported by the data as there are visitors on the weekend as well.
- **The pick-up service is not very popular at this library.** This interpretation is valid as only about 42.42% of the total visits were for picking up.
- **The weekend is the most popular time to visit.** This is true since approximately 62.63% of the visits occurred on the weekend.
Given these analyses, the most accurate interpretation based on marginal relative frequency is **"The weekend is the most popular time to visit."**