An amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball down range.) She hits fourteen balls With driver A and 10 balls with driver B. The drive distances (in yards) for the trials are show below. Assume that the populations are approximately normal. Can you conclude that there is a difference in the Mean drive distances for the two drivers? Use the $\alpha = 0.05$ level of significance.

Question

An amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball down range.) She hits fourteen balls With driver A and 10 balls with driver B. The drive distances (in yards) for the trials are show below.  Assume that the populations are approximately normal. Can you conclude that there is a difference in the Mean drive distances for the two drivers? Use the $\alpha = 0.05$ level of significance.

Quizplus · Accepted Answer

We can conduct a two-sample t-test to compare the means of the two groups. Using a calculator or statistical software, we find a t-value of 2.01 and a p-value of 0.06. Since the p-value is greater than the chosen level of significance (0.05), we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the mean drive distances for the two drivers. However, it is important to note that the sample size for driver B is much smaller than for driver A, which can affect the power of the test and therefore the results.

An Amateur Golfer Wishes to Determine If There Is a Difference