Question

Suppose we are comparing the mean driving distance between 2 types of golf balls. At the same location, the same golfer drives ball A 40 times and ball B 40 times. For the ball A sample there is a mean of 242 yards with a standard deviation of 41 yards. For the ball B sample there is a mean of 265 yards with a standard deviation of 48 yards.   Does the data show that there is a difference in the mean distance between the two balls? Do a hypothesis test showing all steps to make your conclusion.

Answer 1

In this problem, we are to test,

where,




Or, equivalently,

where,


The test statistic is given by:


Under H0,


We reject H0 at level (1 - )*100%

where,


The given data are:
n1 = 40​​​​​
n2 = 40​​​​​








Now,


Hence, we reject H0 at 5% level of significance and conclude that there is significance difference in the mean distance between the two balls.



I hope this clarifies your doubt. If you're satisfied with the solution, hit the Like button. For further clarification, comment below. Thank You. :)