0.75 Use technology to find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion.
0.75 Use technology to find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion.
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
Transcribed Image Text:### Ophthalmology
A study compared the mean electroretinogram (ERG) amplitude of patients with different genetic types of retinitis pigmentosa (RP), a genetic eye disease that often results in blindness. The results are shown in the table below, which were obtained for ln(ERG amplitude) among patients aged 18–29 years.
**Comparison of Mean ln(ERG Amplitude) by Genetic Type among Patients with RP**
| Genetic Type | Mean ± SD | n |
|--------------|-----------|----|
| Dominant | 0.84 ± 0.19 | 63 |
| Recessive | 0.39 ± 0.22 | 34 |
| X-linked | -0.1 ± 0.22 | 29 |
**Instructions:**
- You can use the Inferential Statistics page and the Distribution Calculators page in SALT to answer parts of this question.
**Question (a):**
What is the standard error of ln(ERG amplitude) among patients with dominant RP? (Round your answer to four decimal places.)
**Answer:**
0.0623
**Explanation of Standard Error:**
How does it differ from the standard deviation in the table?
- The standard error reflects the error in the estimate of the mean ln(ERG amplitude) for dominant RP patients, while the standard deviation represents the variation between individual patients with dominant RP.
![### Educational Resource: Statistical Testing for Variance and Mean Differences
#### Section (a)
- **Statement:** The standard error and standard deviation are different names for the same quantity and are actually not different at all.
- **Correct:** This statement is incorrect. The standard error and standard deviation are related but distinct concepts. The standard deviation measures the spread of data points around the mean, while the standard error measures the precision of the sample mean as an estimate of the population mean.
#### Section (b) - Variance Test
- **Question:** What test can be used to compare the variance of ln(ERG amplitude) between patients with dominant vs. recessive RP (Retinitis Pigmentosa)?
- Possible Answers:
- A z test for the equality of two variances.
- A χ² test for the equality of two variances.
- The extreme studentized deviate test for the equality of two variances.
- A t test for the equality of two variances.
- **An F test for the equality of two variances.** *(Correct Choice)*
#### Section (c) - Implementing the Variance Test
- **Task:** Implement the test in (b), and report a p-value (two-tailed) using α = 0.05.
- **Null Hypothesis (H₀):** σ₁² = σ₂²
- **Alternative Hypothesis (H₁):** σ₁² ≠ σ₂²
- **Calculations:**
- **Test Statistic (F):**
\[
\text{F} = \frac{\text{Sd}_1^2}{\text{Sd}_2^2} = \frac{0.019}{0.022} = 0.74586 \approx 0.75
\]
- **Instruction:** Use technology to find the p-value. (Round your answer to four decimal places.)
- **p-value:** [Enter calculated value here]
- **Conclusion Options:**
- Reject H₀: Significant difference in variance.
- **Fail to reject H₀: No significant difference in variance.** *(Correct Choice based on instructions)*
#### Section (d) - Mean Test
- **Question:** What test can be used to compare the mean ln(ERG amplitude) between patients with dominant vs. recessive RP?
- Possible](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeadb183-1175-48ee-be1d-be4cbd36e1e9%2F397ddbd5-8919-4aac-8898-f89ed9ebd7eb%2Fgfkprws_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Resource: Statistical Testing for Variance and Mean Differences
#### Section (a)
- **Statement:** The standard error and standard deviation are different names for the same quantity and are actually not different at all.
- **Correct:** This statement is incorrect. The standard error and standard deviation are related but distinct concepts. The standard deviation measures the spread of data points around the mean, while the standard error measures the precision of the sample mean as an estimate of the population mean.
#### Section (b) - Variance Test
- **Question:** What test can be used to compare the variance of ln(ERG amplitude) between patients with dominant vs. recessive RP (Retinitis Pigmentosa)?
- Possible Answers:
- A z test for the equality of two variances.
- A χ² test for the equality of two variances.
- The extreme studentized deviate test for the equality of two variances.
- A t test for the equality of two variances.
- **An F test for the equality of two variances.** *(Correct Choice)*
#### Section (c) - Implementing the Variance Test
- **Task:** Implement the test in (b), and report a p-value (two-tailed) using α = 0.05.
- **Null Hypothesis (H₀):** σ₁² = σ₂²
- **Alternative Hypothesis (H₁):** σ₁² ≠ σ₂²
- **Calculations:**
- **Test Statistic (F):**
\[
\text{F} = \frac{\text{Sd}_1^2}{\text{Sd}_2^2} = \frac{0.019}{0.022} = 0.74586 \approx 0.75
\]
- **Instruction:** Use technology to find the p-value. (Round your answer to four decimal places.)
- **p-value:** [Enter calculated value here]
- **Conclusion Options:**
- Reject H₀: Significant difference in variance.
- **Fail to reject H₀: No significant difference in variance.** *(Correct Choice based on instructions)*
#### Section (d) - Mean Test
- **Question:** What test can be used to compare the mean ln(ERG amplitude) between patients with dominant vs. recessive RP?
- Possible
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