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

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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
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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