A random sample of 14 golfers was selected from the 14 players on the Ladies Pro

Question

A random sample of 14 golfers was selected from the 14 players on the Ladies Professional Golf Association LPGA low in a recent year. The total amount of money during the year (in dollars) and the scoring average for each player in the sample was recorded. Lower scoring averages are better in golf. the below displays the relationship between money and scoring average for these 14 players. Explain why it would not be appropriate to construct a confidence interval for the slope of the least-squares regression line relating money to scoring average. of the natural logarithm of money versus average is shown at top right along with some computer output for a least-squares regression using the transformed data. (b) Predict the amount of money won for an LPGA golfer with a scoring average of 70. (c) Calculate and interpret a 95% confidence interval for the slope of the least-squares regression line relating In(money) to scoring average. Assume that the conditions for interference have been met. After you finish, you can view two example solutions on the book's Web site (www.whfreeman.com/tps5e). Determine whether you think each solution is "complete," "substantial," "developing," or "minimal." If the solution is not complete, what improvements would you suggest to the student who wrote it? Finally, your teacher will provide you with a scoring rubric. Score your response and note what, if anything, you would do differently to improve your own score.

Explanation / Answer

b ) The regression equation as can be seen from the output table is

LPGA = 77.53 -0.904*ScoringAverage , putting scoring average = 70 we get

77.53 -0.904*70 = 14.25

c) we are given SE as 0.096

so the confidence interval is given as

slope +- Z*SE , now for 95% CI , we see the z multiplier as 1.96

-0.904 +- 1.96*0.096

(-1.09,-0.71) , this means that we are 95% confident in saying that the true value of the slope would lie between -1.09 and -0.71

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