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.)

We are conducting a hypothesis test to determine if the standard deviation (\(\sigma\)) of the diameters of the golf balls is less than 0.004 inches, as required by the professional golfing association. Since the population is assumed to be normally distributed, this is a one-tailed test for the population standard deviation. 

The hypotheses for this test are as follows:

- **Null Hypothesis \(H_0\)**: \(\sigma = 0.004\) (The standard deviation is equal to 0.004 inches, implying no evidence that the standard deviation is less than the requirement.)
- **Alternative Hypothesis \(H_1\)**: \(\sigma < 0.004\) (The standard deviation is less than 0.004 inches, meeting the requirement.)

### Notation:

- \(H_0\): \(\sigma = 0.004\)
- \(H_1\): \(\sigma < 0.004\)

This is a left-tailed hypothesis test because we are testing if the standard deviation is **less than** the specified value.

Do you want to proceed with the calculation of the test statistic and decision rule for the hypothesis test?

### Additional Questions:
1. How do we calculate the sample standard deviation?
2. What distribution should be used to test hypotheses about population variance?
3. How do we determine the critical value at \(\alpha = 0.10\)?
4. What is the difference between a one-tailed and two-tailed test?
5. How does sample size affect the test for standard deviation?

#### Tip:
When testing for variance or standard deviation, always use the chi-squared distribution if the population is assumed to be normally distributed.

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?

Conduct a hypothesis test to check if the standard deviation of golf ball diameters is less than 0.004 inches at a 0.10 level of significance. Learn how to apply the chi-square distribution to test population variance and standard deviation assumptions in this statistics problem.

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