MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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How can I find the 95% confidence interval and test statistics using excel or statcrunch. Thank You
![### Hypothesis Testing for Equality of Proportions
In a study of the success rate of challenging referee calls, it's observed that men challenged a total of 1940 calls, with the result that 42% of these calls were overturned. On the other hand, women challenged 763 referee calls, out of which 221 calls were overturned. This statistical analysis aims to test the claim at a 0.05 significance level that men and women have equal success in challenging calls.
**Key components of the analysis include:**
1. **Sample Sizes and Successes:**
- Men: 1940 calls challenged, 42% success rate.
- Women: 763 calls challenged, 221 calls overturned.
2. **Testing the Claim:**
- Null Hypothesis (\(H_0\)): Men and women have equal success rates in challenging calls.
- Alternative Hypothesis (\(H_1\)): Men and women have different success rates in challenging calls.
3. **Confidence Interval Calculation:**
- A 95% confidence interval is constructed for the difference in proportions (\(p_1 - p_2\)) where \(p_1\) and \(p_2\) are the success rates for men and women, respectively.
- The confidence interval is represented as:
\[
\boxed{} \,<\, (p_1 - p_2) \,<\, \boxed{}
\]
- (Values to be rounded to three decimal places as needed.)
4. **Conclusion:**
- Based on whether the confidence interval contains zero, a conclusion will be drawn regarding the equality of success rates between men and women.
This statistical approach helps in understanding whether there is a statistically significant difference in the success rates of men and women when they challenge referee calls.](https://content.bartleby.com/qna-images/question/242a0dac-d7d5-4e5c-b656-00cdaf0b077c/0d6f8888-0ed3-4e1b-b1d0-4e07b82d7622/m9jdy6.png)
Transcribed Image Text:### Hypothesis Testing for Equality of Proportions
In a study of the success rate of challenging referee calls, it's observed that men challenged a total of 1940 calls, with the result that 42% of these calls were overturned. On the other hand, women challenged 763 referee calls, out of which 221 calls were overturned. This statistical analysis aims to test the claim at a 0.05 significance level that men and women have equal success in challenging calls.
**Key components of the analysis include:**
1. **Sample Sizes and Successes:**
- Men: 1940 calls challenged, 42% success rate.
- Women: 763 calls challenged, 221 calls overturned.
2. **Testing the Claim:**
- Null Hypothesis (\(H_0\)): Men and women have equal success rates in challenging calls.
- Alternative Hypothesis (\(H_1\)): Men and women have different success rates in challenging calls.
3. **Confidence Interval Calculation:**
- A 95% confidence interval is constructed for the difference in proportions (\(p_1 - p_2\)) where \(p_1\) and \(p_2\) are the success rates for men and women, respectively.
- The confidence interval is represented as:
\[
\boxed{} \,<\, (p_1 - p_2) \,<\, \boxed{}
\]
- (Values to be rounded to three decimal places as needed.)
4. **Conclusion:**
- Based on whether the confidence interval contains zero, a conclusion will be drawn regarding the equality of success rates between men and women.
This statistical approach helps in understanding whether there is a statistically significant difference in the success rates of men and women when they challenge referee calls.
![### Statistical Analysis of Tennis Referee Challenges by Gender
**Objective:**
To analyze the effectiveness of challenges made by men and women at a major tennis tournament using an instant replay system. The goal is to test the claim that men and women have equal success in challenging referee calls.
**Data Summary:**
- **Men's Challenges:**
- Total challenges: 1424
- Overturned calls: 425
- **Women's Challenges:**
- Total challenges: 753
- Overturned calls: 221
**Statistical Analysis:**
Given the above data, we will use a 0.05 significance level to test the hypothesis that men and women have equal success rates when challenging referee calls.
To do this, we calculate the 95% confidence interval for the difference in proportions of successful challenges between men and women.
**Confidence Interval:**
\[ \text{The 95% confidence interval is } [ \, \_\_ \, < (p_1 - p_2) < \, \_\_ \, ] \]
(Round to three decimal places as needed.)
**Explanation:**
- \( p_1 \): Proportion of successful challenges by men.
- \( p_2 \): Proportion of successful challenges by women.
- The interval will give us a range of values within which the true difference between men’s and women’s success rates is expected to lie, with 95% confidence.
**Next Steps:**
1. Calculate the sample proportions of overturned calls for both men ( \( \frac{425}{1424} \) ) and women ( \( \frac{221}{753} \) ).
2. Use these sample proportions to compute the standard error of the difference in proportions.
3. Determine the critical value for a 95% confidence level.
4. Calculate the confidence interval.
This analysis will help us understand if there is a statistically significant difference in the success rates of men and women when challenging referee calls using the instant replay system in tennis.](https://content.bartleby.com/qna-images/question/242a0dac-d7d5-4e5c-b656-00cdaf0b077c/0d6f8888-0ed3-4e1b-b1d0-4e07b82d7622/vou5xx8.png)
Transcribed Image Text:### Statistical Analysis of Tennis Referee Challenges by Gender
**Objective:**
To analyze the effectiveness of challenges made by men and women at a major tennis tournament using an instant replay system. The goal is to test the claim that men and women have equal success in challenging referee calls.
**Data Summary:**
- **Men's Challenges:**
- Total challenges: 1424
- Overturned calls: 425
- **Women's Challenges:**
- Total challenges: 753
- Overturned calls: 221
**Statistical Analysis:**
Given the above data, we will use a 0.05 significance level to test the hypothesis that men and women have equal success rates when challenging referee calls.
To do this, we calculate the 95% confidence interval for the difference in proportions of successful challenges between men and women.
**Confidence Interval:**
\[ \text{The 95% confidence interval is } [ \, \_\_ \, < (p_1 - p_2) < \, \_\_ \, ] \]
(Round to three decimal places as needed.)
**Explanation:**
- \( p_1 \): Proportion of successful challenges by men.
- \( p_2 \): Proportion of successful challenges by women.
- The interval will give us a range of values within which the true difference between men’s and women’s success rates is expected to lie, with 95% confidence.
**Next Steps:**
1. Calculate the sample proportions of overturned calls for both men ( \( \frac{425}{1424} \) ) and women ( \( \frac{221}{753} \) ).
2. Use these sample proportions to compute the standard error of the difference in proportions.
3. Determine the critical value for a 95% confidence level.
4. Calculate the confidence interval.
This analysis will help us understand if there is a statistically significant difference in the success rates of men and women when challenging referee calls using the instant replay system in tennis.
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