Can you explain how you would know to use t for this problem, using Excel's = confidence.t function instead of = confidence.norm?
Can you explain how you would know to use t for this problem, using Excel's = confidence.t function instead of = confidence.norm?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Can you explain how you would know to use t for this problem, using Excel's = confidence.t
![**Educational Content on Constructing Confidence Intervals: Analysis of Hollywood Movie Lengths**
**Scenario Overview:**
We are analyzing a random sample of 35 Hollywood movies made in the last 10 years. The sample has an average movie length of 125.2 minutes with a standard deviation of 20.4 minutes.
**Tasks:**
**a) Construct a 95% confidence interval for the true mean length of all Hollywood movies made in the last 10 years.**
**b) Evaluate a claim regarding the Bourne film series:**
As of January 2017, five Bourne movies have an average length of 119.8 minutes. The claim is that the mean length of Bourne movies is greater than the mean length of all Hollywood movies. Analyze if the confidence interval supports or contradicts this claim.
---
**Detailed Analysis:**
**Given Data:**
- Sample size (n) = 35
- Sample mean (\(\bar{x}\)) = 125.2
- Standard deviation (s) = 20.4
**a) Confidence Interval Calculation:**
1. **Confidence Level:** 95%
2. **Level of Significance (\(\alpha\)):** \(1 - 0.95 = 0.05\)
3. **Two-tailed test (\(\alpha/2\)):** 0.025
4. **Degrees of Freedom (df):** \(n - 1 = 34\)
To find the critical value of t at 34 degrees of freedom, use the Excel function:
\[
=T.INV(0.975, 34)
\]
Result: **2.032245**
5. **Confidence Interval (CI) Calculation:**
\[
CI = \bar{x} \pm t \times \left(\frac{s}{\sqrt{n}}\right)
\]
\[
CI = 125.2 \pm 2.032245 \times \left(\frac{20.4}{\sqrt{35}}\right)
\]
\[
CI \approx (118.1924, 132.2076)
\]
**b) Hypothesis Testing:**
- **Null Hypothesis (\(H_0\)):** \(\mu \leq 119.8\)
- **Alternative Hypothesis (\(H_1\)):** \(\mu >](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0792917d-61c4-4ae7-a8dc-3ece8fbf5987%2F9f6d9dc3-cca5-45e9-b731-aaff8c3fc31b%2Fetj0r0k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content on Constructing Confidence Intervals: Analysis of Hollywood Movie Lengths**
**Scenario Overview:**
We are analyzing a random sample of 35 Hollywood movies made in the last 10 years. The sample has an average movie length of 125.2 minutes with a standard deviation of 20.4 minutes.
**Tasks:**
**a) Construct a 95% confidence interval for the true mean length of all Hollywood movies made in the last 10 years.**
**b) Evaluate a claim regarding the Bourne film series:**
As of January 2017, five Bourne movies have an average length of 119.8 minutes. The claim is that the mean length of Bourne movies is greater than the mean length of all Hollywood movies. Analyze if the confidence interval supports or contradicts this claim.
---
**Detailed Analysis:**
**Given Data:**
- Sample size (n) = 35
- Sample mean (\(\bar{x}\)) = 125.2
- Standard deviation (s) = 20.4
**a) Confidence Interval Calculation:**
1. **Confidence Level:** 95%
2. **Level of Significance (\(\alpha\)):** \(1 - 0.95 = 0.05\)
3. **Two-tailed test (\(\alpha/2\)):** 0.025
4. **Degrees of Freedom (df):** \(n - 1 = 34\)
To find the critical value of t at 34 degrees of freedom, use the Excel function:
\[
=T.INV(0.975, 34)
\]
Result: **2.032245**
5. **Confidence Interval (CI) Calculation:**
\[
CI = \bar{x} \pm t \times \left(\frac{s}{\sqrt{n}}\right)
\]
\[
CI = 125.2 \pm 2.032245 \times \left(\frac{20.4}{\sqrt{35}}\right)
\]
\[
CI \approx (118.1924, 132.2076)
\]
**b) Hypothesis Testing:**
- **Null Hypothesis (\(H_0\)):** \(\mu \leq 119.8\)
- **Alternative Hypothesis (\(H_1\)):** \(\mu >
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