A professional golf player considers accepting a sponsorship offer from a new equipment company which requires the

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Question:

A professional golf player considers accepting a sponsorship offer from a new equipment company which requires the use of its product for the next several years. He first wants to see whether the new club he would use can send the ball at least as far as his current club. The driver carry distance of his current club is 300 yards on average, with a standard deviation of 10 yards. He believes the standard deviation from the new club will be the same.

He wants to accept the offer (because he can make extra money!) as long as he doesn’t find any evidence that the new club sends the ball a shorter distance than 300 yards on average. To help him perform a hypothesis test, write the appropriate hypotheses below. Let µ be the average carry distance he can send using the new club.

H0 : 300 Ha : u<300

Construct the 95% two-sided confidence interval of the mean driving distance of new club using x¯ = 296.1 and σ = 10.