Final answer:
The null hypothesis represents the claim that the standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes, symbolically H0: σ ≤ 3.5. The alternative hypothesis suggests it is more than 3.5 strokes, Ha: σ > 3.5, indicating that a right-tailed test is appropriate.
Step-by-step explanation:
The null hypothesis (H0) and alternative hypothesis (Ha) are a crucial part of hypothesis testing in statistics. When a claim is made about a population parameter, such as the standard deviation or mean, we set up a null hypothesis that the parameter is equal to a certain value and an alternative hypothesis that states what we are testing for (more than, less than, or not equal to the claimed value).
In the scenario provided, where a golf analyst claims that the standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes, the correct null hypothesis in words is, "the standard deviation of the 18-hole scores for a golfer is at most 3.5 strokes." Symbolically, this can be expressed as H0: σ ≤ 3.5. Since the claim is "at most," we are interested in finding out if the standard deviation is higher than this value. Consequently, the alternative hypothesis in words would be, "the standard deviation of the 18-hole scores for a golfer is more than 3.5 strokes," and symbolically, it is Ha: σ > 3.5.
Given that the alternative hypothesis is looking for a value greater than 3.5, the hypothesis test for this claim is a right-tailed test. This type of test is used because we are only interested in the upper part (the right tail) of the distribution where the standard deviation values would be above 3.5 if the null hypothesis is false.