Part 2 of 3 (b) Construct a 90% confidence interval for the proportion of strikes that are critical strikes. Round the answers to at least three decimal places. A 90% confidence interval for the proportion of strikes that are critical strikes is 0
Part 2 of 3 (b) Construct a 90% confidence interval for the proportion of strikes that are critical strikes. Round the answers to at least three decimal places. A 90% confidence interval for the proportion of strikes that are critical strikes is 0
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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![**Confidence Intervals in Probability of Critical Strikes**
In the computer game *League of Legends*, some of the strikes are critical strikes, which do more damage. Assume that the probability of a critical strike is the same for every attack and that attacks are independent. Assume that a character has 244 critical strikes out of 593 attacks.
### Part 1 of 3
**(a) Construct an 80% confidence interval for the proportion of strikes that are critical strikes. Round the answers to at least three decimal places.**
An 80% confidence interval for the proportion of strikes that are critical strikes is:
\[ 0.386 < p < 0.437 \]
**Alternate Answer:**
An 80% confidence interval for the proportion of strikes that are critical strikes is \( 0.386 < p < 0.437 \).
A progress bar is displayed indicating completion as "Part: 1/3".
### Part 2 of 3
**(b) Construct a 90% confidence interval for the proportion of strikes that are critical strikes. Round the answers to at least three decimal places.**
A 90% confidence interval for the proportion of strikes that are critical strikes is:
\[ \quad < p < \quad \].
### Explanation:
To construct confidence intervals, we use the formula for a confidence interval for a proportion:
\[ \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]
where:
- \(\hat{p}\) = Sample proportion
- \(Z\) = Z-value for the desired confidence level
- \(n\) = Sample size
For example, an 80% confidence interval uses the Z-value corresponding to 80% confidence level. The calculated interval will give the range within which we are 80% confident the true proportion of critical strikes lies.
**Note:**
The images should typically have detailed descriptions of any graphs or numerical results as seen to aid understanding, even if this involves algebraic expression or statistical tables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29a07bd8-eb1c-498d-b0a8-9eb9d6fddf09%2Fe083dbb3-0ab5-4c89-861f-3c0186a3af25%2F7kyyyjk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Confidence Intervals in Probability of Critical Strikes**
In the computer game *League of Legends*, some of the strikes are critical strikes, which do more damage. Assume that the probability of a critical strike is the same for every attack and that attacks are independent. Assume that a character has 244 critical strikes out of 593 attacks.
### Part 1 of 3
**(a) Construct an 80% confidence interval for the proportion of strikes that are critical strikes. Round the answers to at least three decimal places.**
An 80% confidence interval for the proportion of strikes that are critical strikes is:
\[ 0.386 < p < 0.437 \]
**Alternate Answer:**
An 80% confidence interval for the proportion of strikes that are critical strikes is \( 0.386 < p < 0.437 \).
A progress bar is displayed indicating completion as "Part: 1/3".
### Part 2 of 3
**(b) Construct a 90% confidence interval for the proportion of strikes that are critical strikes. Round the answers to at least three decimal places.**
A 90% confidence interval for the proportion of strikes that are critical strikes is:
\[ \quad < p < \quad \].
### Explanation:
To construct confidence intervals, we use the formula for a confidence interval for a proportion:
\[ \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]
where:
- \(\hat{p}\) = Sample proportion
- \(Z\) = Z-value for the desired confidence level
- \(n\) = Sample size
For example, an 80% confidence interval uses the Z-value corresponding to 80% confidence level. The calculated interval will give the range within which we are 80% confident the true proportion of critical strikes lies.
**Note:**
The images should typically have detailed descriptions of any graphs or numerical results as seen to aid understanding, even if this involves algebraic expression or statistical tables.
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