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The standard deviation of the paired differences is approximately \( 2.8 \) (rounded to one decimal place).

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Here are five related questions to expand your understanding:

1. How is the standard deviation of differences used in hypothesis testing?
2. What is the null hypothesis in this type of paired sample t-test?
3. Why is it important to check if the differences are normally distributed?
4. How does changing the significance level (\(\alpha\)) affect the test result?
5. How would the interpretation change if the new scores were higher than the old ones?

**Tip:** In a paired sample test, focusing on the differences between paired data points is key to eliminating the variability between subjects and focusing solely on the treatment effect.

A golf club manufacturer claims that golfers can lower their scores by using the manufacturer's newly designed golf clubs. Eight golfers are randomly selected, and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are asked again to give their most recent score. The scores for each golfer are given. Is there enough evidence to support the manufacturer's claim?

This problem explores a hypothesis test using a paired t-test to analyze whether a golf club manufacturer's newly designed clubs improve golfer scores. The data includes scores before and after using the new design, and the problem focuses on calculating the standard deviation of paired differences.

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