MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.](https://content.bartleby.com/qna-images/question/06a9a237-982c-465e-8a17-4be5fc663e3e/9d66664a-90ce-475c-a268-5797d786f0d8/1sds8gm_processed.jpeg)
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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