Suppose a professional golfing association requires that the standard deviation of the diameter of a golf ball be less than 0.004 inch. Determine whether these randomly selected golf balls conform to this requirement at the alpha equals 0.10 level of significance. Assume that the population is normally distributed. 1.681
1.683
1.681
1.677
1.681
1.684
1.682
1.677
1.684
1.679
1.679
1.684 What are the correct hypotheses for this​ test?
H Subscript 0​: 
▼ 
p
mu
sigma
▼ 
not equals
greater than
less than
equals
  
enter your response here versus H Subscript 1​: 
▼ 
p
mu
sigma
▼ 
not equals
greater than
equals
less than
  
enter your response here
​(Type integers or decimals. Do not​ round.)

This problem involves testing whether the standard deviation \( \sigma \) of the golf ball diameters is less than 0.004 inches. Since we are dealing with the population standard deviation, this requires a **chi-square test for a single population variance**. 

Here is the correct setup of the hypotheses:

### **Hypotheses:**
- **Null hypothesis \( H_0 \):** \( \sigma = 0.004 \)  
  (The standard deviation is equal to 0.004, meaning the balls may not meet the requirement.)
- **Alternative hypothesis \( H_1 \):** \( \sigma < 0.004 \)  
  (The standard deviation is less than 0.004, meaning the balls meet the association's requirement.)

This is a **one-tailed, lower-tailed test** since the association wants to confirm that the standard deviation is **less than** 0.004 inches.

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Would you like me to calculate the chi-square test statistic for this problem using your data and determine whether the null hypothesis should be rejected at the \( \alpha = 0.10 \) level? 

Here are five related questions that expand on this topic:
1. What is the formula for the chi-square test statistic for variance?
2. How do you determine the critical value for a one-tailed chi-square test?
3. How do you interpret the result of a chi-square test?
4. What assumptions must be satisfied for the chi-square test to be valid?
5. What alternative tests can be used if the population is not normally distributed?

**Tip:** Always check the normality assumption when applying chi-square tests on variance, as this test is sensitive to non-normality.

Suppose a professional golfing association requires that the standard deviation of the diameter of a golf ball be less than 0.004 inch. Determine whether these randomly selected golf balls conform to this requirement at the alpha equals 0.10 level of significance. Assume that the population is normally distributed. 1.681, 1.683, 1.681, 1.677, 1.681, 1.684, 1.682, 1.677, 1.684, 1.679, 1.679, 1.684. What are the correct hypotheses for this test? H0: (σ = 0.004) versus H1: (σ < 0.004)

Determine if the standard deviation of golf ball diameters is less than 0.004 inch using a chi-square test for variance at the 0.10 level of significance. This detailed example guides you through hypothesis testing, including setting up hypotheses and calculating the chi-square test statistic for normally distributed populations.

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