### Question 5 Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. 1. **Check the conditions of the Central Limit Theorem for this scenario.** 2. **Calculate the number of expected successes.** --- This question is part of a statistics or probability module focused on hypothesis testing and the application of the Central Limit Theorem in a real-world scenario. **Explanation:** - **Central Limit Theorem Conditions:** To apply the Central Limit Theorem (CLT), the sample size should be large enough (usually \( n ≥ 30 \)), the samples should be independent, and the success-failure condition should hold (both np and n(1-p) should be at least 10). - **Number of Expected Successes:** The expected number of successes (E) can be calculated as: \[ E = n \times p \] where \( n \) is the total number of trials (free-throw attempts in this context) and \( p \) is the historical success rate (53.3%).
### Question 5 Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. 1. **Check the conditions of the Central Limit Theorem for this scenario.** 2. **Calculate the number of expected successes.** --- This question is part of a statistics or probability module focused on hypothesis testing and the application of the Central Limit Theorem in a real-world scenario. **Explanation:** - **Central Limit Theorem Conditions:** To apply the Central Limit Theorem (CLT), the sample size should be large enough (usually \( n ≥ 30 \)), the samples should be independent, and the success-failure condition should hold (both np and n(1-p) should be at least 10). - **Number of Expected Successes:** The expected number of successes (E) can be calculated as: \[ E = n \times p \] where \( n \) is the total number of trials (free-throw attempts in this context) and \( p \) is the historical success rate (53.3%).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Question 5
Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level.
1. **Check the conditions of the Central Limit Theorem for this scenario.**
2. **Calculate the number of expected successes.**
---
This question is part of a statistics or probability module focused on hypothesis testing and the application of the Central Limit Theorem in a real-world scenario.
**Explanation:**
- **Central Limit Theorem Conditions:**
To apply the Central Limit Theorem (CLT), the sample size should be large enough (usually \( n ≥ 30 \)), the samples should be independent, and the success-failure condition should hold (both np and n(1-p) should be at least 10).
- **Number of Expected Successes:**
The expected number of successes (E) can be calculated as:
\[
E = n \times p
\]
where \( n \) is the total number of trials (free-throw attempts in this context) and \( p \) is the historical success rate (53.3%).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fecf56a-cd1b-4ba2-83c3-6deee4a86d70%2Fdc1723a0-0370-48c4-8d8b-036c893c8a4b%2Fl3ypixt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 5
Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level.
1. **Check the conditions of the Central Limit Theorem for this scenario.**
2. **Calculate the number of expected successes.**
---
This question is part of a statistics or probability module focused on hypothesis testing and the application of the Central Limit Theorem in a real-world scenario.
**Explanation:**
- **Central Limit Theorem Conditions:**
To apply the Central Limit Theorem (CLT), the sample size should be large enough (usually \( n ≥ 30 \)), the samples should be independent, and the success-failure condition should hold (both np and n(1-p) should be at least 10).
- **Number of Expected Successes:**
The expected number of successes (E) can be calculated as:
\[
E = n \times p
\]
where \( n \) is the total number of trials (free-throw attempts in this context) and \( p \) is the historical success rate (53.3%).
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