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.