4. A survey of State U students asked if they were satisfied with the way the school has handled class scheduling during the pandemic. 51.3% of the respondents were female, 82% replied, "no," and 46.1% fell into both categories. Are the events female and no independent? Justify your response.
4. A survey of State U students asked if they were satisfied with the way the school has handled class scheduling during the pandemic. 51.3% of the respondents were female, 82% replied, "no," and 46.1% fell into both categories. Are the events female and no independent? Justify your response.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Question 4
Please use simple probability rules
![**Survey Analysis of State U Students' Satisfaction with Class Scheduling During the Pandemic**
A study was conducted to gauge the satisfaction levels among students of State U regarding the institution's handling of class schedules during the COVID-19 pandemic. The results of the survey revealed the following key statistics:
- 51.3% of the respondents identified as female.
- 82% of all respondents expressed dissatisfaction, responding with "no" to the satisfaction query.
- 46.1% of the respondents were both female and expressed dissatisfaction ("no").
**Statistical Question for Analysis:**
Are the events "female" and "no" independent? Justify your response.
**Explanation:**
To determine if the events "female" (F) and "no" (N) are independent, we need to compare the joint probability of these events with the product of their individual probabilities.
- Probability of being female, P(F) = 0.513
- Probability of replying "no," P(N) = 0.820
- Joint probability of being female and replying "no," P(F ∩ N) = 0.461
For events to be independent, the following condition must hold:
\[ P(F ∩ N) = P(F) \times P(N) \]
Plugging in the given values:
\[ 0.461 = 0.513 \times 0.820 \]
\[ 0.461 ≈ 0.420 \]
Since \( 0.461 \) is not equal to \( 0.420 \), the events "female" and "no" are not independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06a9a237-982c-465e-8a17-4be5fc663e3e%2F9d66664a-90ce-475c-a268-5797d786f0d8%2F1sds8gm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Survey Analysis of State U Students' Satisfaction with Class Scheduling During the Pandemic**
A study was conducted to gauge the satisfaction levels among students of State U regarding the institution's handling of class schedules during the COVID-19 pandemic. The results of the survey revealed the following key statistics:
- 51.3% of the respondents identified as female.
- 82% of all respondents expressed dissatisfaction, responding with "no" to the satisfaction query.
- 46.1% of the respondents were both female and expressed dissatisfaction ("no").
**Statistical Question for Analysis:**
Are the events "female" and "no" independent? Justify your response.
**Explanation:**
To determine if the events "female" (F) and "no" (N) are independent, we need to compare the joint probability of these events with the product of their individual probabilities.
- Probability of being female, P(F) = 0.513
- Probability of replying "no," P(N) = 0.820
- Joint probability of being female and replying "no," P(F ∩ N) = 0.461
For events to be independent, the following condition must hold:
\[ P(F ∩ N) = P(F) \times P(N) \]
Plugging in the given values:
\[ 0.461 = 0.513 \times 0.820 \]
\[ 0.461 ≈ 0.420 \]
Since \( 0.461 \) is not equal to \( 0.420 \), the events "female" and "no" are not independent.
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