Question

A golf instruction company claims that players who use their newly-designed clubs have improved scores (which means a decrease in score). The average golf scores of eight randomly selected golfers were reported before and after using the new clubs.

Let d = score before new clubs – score after new clubs.
State the null hypothesis and alternative hypothesis. Explain your reasoning

Answer 1

The null hypothesis (H0) for the golf score improvement study is that the average difference in golf scores before and after using new clubs is less than or equal to zero. The alternative hypothesis (H1) is that this average difference is greater than zero, signifying an improvement in scores.

Step-by-step explanation:

The question pertains to formulating a hypothesis test in the context of determining whether the use of newly-designed golf clubs results in improved scores for players. When defining the hypotheses for a hypothesis test, the null hypothesis (H0) typically represents the status quo or a statement of no effect, while the alternative hypothesis (H1 or Ha) represents what we are trying to find evidence for, in this case, an improvement in golf scores.

Given that improvement in golf scores means a decrease in the number of strokes required to complete a course, the variable 'd' represents the difference in scores before and after using the new clubs (score before – score after). If the golf instruction company's claim is true, we expect 'd' to be positive because the score before should be higher than the score after using the new clubs.

The null hypothesis would be stated as H0: μ_d ≤ 0, which posits that the mean difference in scores (before minus after) is less than or equal to zero, indicating no improvement or a worsening of scores.

Conversely, the alternative hypothesis is H1: μ_d > 0, suggesting that the mean difference is greater than zero, and therefore, indicating an improvement in scores with the new clubs.