Question

1. An old say in golf is “you drive for show and you putt for dough”. The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data on the top 69 money winners on the PGA tour in 1993 were examined. The average number of putts per hole for each player is used to predict their total winnings using the simple linear regression model:                     

       1993 winnings_i = β0 + β1(average number of putts per hole)i + εi

           R² = 0.081, s = 281,000   

           Variable                      Parameter Est.                Std. Err. Of Parameter Est.

            Constant                     7,897,179                        3,023,782

            Avg. Putts                 -4,139,198                        1,698,371

Suppose that the researchers desire to test the hypothesis that there is a significant negative relationship between 1993 winnings and the average number of putts per hole.

Use a= 0.05.

1. State H₀ and H_a.                                                                                                                             
2. Find the test statistic. Show work.                                                                                            
3. Find the p-value.                                                                                                            
4. Make the decision to reject or not to reject the null hypothesis.                                         
5. Summarize the results in terms of the original claim.

Answer 1

Result:

1. An old say in golf is “you drive for show and you putt for dough”. The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data on the top 69 money winners on the PGA tour in 1993 were examined. The average number of putts per hole for each player is used to predict their total winnings using the simple linear regression model:                     

       1993 winningsi = β0 + β1(average number of putts per hole)i + εi

           R2 = 0.081, s = 281,000   

           Variable                      Parameter Est.                Std. Err. Of Parameter Est.

            Constant                     7,897,179                        3,023,782

            Avg. Putts                 -4,139,198                        1,698,371

Suppose that the researchers desire to test the hypothesis that there is a significant negative relationship between 1993 winnings and the average number of putts per hole.

Use a= 0.05.

State H0 and Ha.                                                                                                                             

 H0: β1 = 0   

 H1: β1 <  0   

This is a lower tail test

Find the test statistic. Show work.                                                                                            

 t = -4139198/1698371

= -2.4372

Find the p-value.     

Df= 69-2=67

P value = 0.0087       

Excel function used to get probability: =T.DIST(-2.4372,67,TRUE)                                                                                               

Make the decision to reject or not to reject the null hypothesis.                                         

Since obtained p value 0.0087 < alpha level 0.05.

We reject the null hypothesis.

Summarize the results in terms of the original claim.

There is sufficient evidence to conclude that there is a significant negative relationship between 1993 winnings and the average number of putts per hole.