Suppose a professional golfing association requires that the standard deviation of the diameter of a golf ball be less than 0.005 inch. Determine whether these randomly selected golf balls conform to this requirement at the α = 0.01 level of significance. Assume that the population is normally distributed. Click the icon to view the chi-square distribution table. What are the correct hypotheses for this test? Ho: 00 versus H₁: ▼ (Type integers or decimals. Do not round.) 1.684 1.684 1.683 1.683 1.677 1.683 1.683 1.677 1.684 1.678 1.681 1.677 4
Suppose a professional golfing association requires that the standard deviation of the diameter of a golf ball be less than 0.005 inch. Determine whether these randomly selected golf balls conform to this requirement at the α = 0.01 level of significance. Assume that the population is normally distributed. Click the icon to view the chi-square distribution table. What are the correct hypotheses for this test? Ho: 00 versus H₁: ▼ (Type integers or decimals. Do not round.) 1.684 1.684 1.683 1.683 1.677 1.683 1.683 1.677 1.684 1.678 1.681 1.677 4
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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![**Chi-Square Test for Standard Deviation Conformity of Golf Balls**
**Scenario:**
A professional golfing association mandates that the standard deviation of the diameter of a golf ball must be less than 0.005 inches. You need to determine if the selected golf balls meet this requirement at a significance level of α = 0.01. Assume the population is normally distributed.
**Steps to Follow:**
1. **Data Collection:**
The diameters (in inches) of the selected golf balls are as follows:
- 1.684, 1.684, 1.683
- 1.683, 1.677, 1.683
- 1.683, 1.677, 1.684
- 1.678, 1.681, 1.677
2. **Hypotheses Formulation:**
Determine the null (H₀) and alternative hypotheses (H₁):
- \( H_0: σ = \text{hypothesized standard deviation (0.005 inches)} \)
- \( H_1: σ < \text{hypothesized standard deviation (0.005 inches)} \)
Here, "σ" represents the population standard deviation.
3. **Chi-Square Distribution Table:**
Refer to the chi-square distribution table to find the critical value for a given degrees of freedom at the specified level of significance.
4. **Chi-Square Test Statistic Calculation:**
Calculate the test statistic using the formula:
\[ χ^2 = \frac{(n - 1)s^2}{σ^2} \]
Where:
- \( n \) = Sample size
- \( s^2 \) = Sample variance
- \( σ^2 \) = Hypothesized population variance
5. **Conclusion:**
Compare the Chi-square test statistic with the critical value from the chi-square distribution table. Based on the comparison, determine whether to accept or reject the null hypothesis.
**User Interaction:**
- **Input Fields:**
- H₀ and H₁ hypothesis inputs
- Fields to enter integers or decimals for hypotheses
- **Buttons/Links:**
- "Help me solve this" for guided steps
- "View an example" for sample problems
- "Get more help" for additional resources](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2241529c-3605-4343-8b09-279b4f80df33%2F8fa0f2c7-a934-48cd-9207-ae878c715d22%2Fcn1pkr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Chi-Square Test for Standard Deviation Conformity of Golf Balls**
**Scenario:**
A professional golfing association mandates that the standard deviation of the diameter of a golf ball must be less than 0.005 inches. You need to determine if the selected golf balls meet this requirement at a significance level of α = 0.01. Assume the population is normally distributed.
**Steps to Follow:**
1. **Data Collection:**
The diameters (in inches) of the selected golf balls are as follows:
- 1.684, 1.684, 1.683
- 1.683, 1.677, 1.683
- 1.683, 1.677, 1.684
- 1.678, 1.681, 1.677
2. **Hypotheses Formulation:**
Determine the null (H₀) and alternative hypotheses (H₁):
- \( H_0: σ = \text{hypothesized standard deviation (0.005 inches)} \)
- \( H_1: σ < \text{hypothesized standard deviation (0.005 inches)} \)
Here, "σ" represents the population standard deviation.
3. **Chi-Square Distribution Table:**
Refer to the chi-square distribution table to find the critical value for a given degrees of freedom at the specified level of significance.
4. **Chi-Square Test Statistic Calculation:**
Calculate the test statistic using the formula:
\[ χ^2 = \frac{(n - 1)s^2}{σ^2} \]
Where:
- \( n \) = Sample size
- \( s^2 \) = Sample variance
- \( σ^2 \) = Hypothesized population variance
5. **Conclusion:**
Compare the Chi-square test statistic with the critical value from the chi-square distribution table. Based on the comparison, determine whether to accept or reject the null hypothesis.
**User Interaction:**
- **Input Fields:**
- H₀ and H₁ hypothesis inputs
- Fields to enter integers or decimals for hypotheses
- **Buttons/Links:**
- "Help me solve this" for guided steps
- "View an example" for sample problems
- "Get more help" for additional resources
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