General Instructions on Project: Download and save both problem (Word) file and data (Excel) file

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General Instructions on Project:

• Download and save both problem (Word) file and data (Excel) file.  Work on them: type your answer under each problem in the Word file and make your Excel output in the Excel file.  SAVE!
• Please name your file using your name (last-first.xslx) but don’t need to name each worksheet within your Excel file because Canvas shows your file as one long scroll of worksheets.
• Submit (post) both files to the submission link of Project module in Canvas by 11:55pm, Sunday, Dec. 6, 2020.
• You can post multiple times by due time, but recent posting replaces previous posting.  Therefore, please make sure to post complete version.  Grading will begin after submission link closes. 

• This project requires the understanding of chapters 11, 4.8, and 13:  these are Canvas module weeks 11 and 13 content.  
• Please make sure that your Excel is full-version equipped with Data Analysis.   If not sure, check the file “Bring Add-Ins Analysis Toolpack to Excel” from Practice Excel… module of Canvas.
• For specific functions (skill) of Excel, practice Excel procedures with “practice” file. You will run same procedures with “project” data in this project. 

Excel Demo videos in Canvas show how to run each Excel analysis function “practice (not project)” data.  Apply the skills in analyzing project data.  Application and interpretation are the purposes of this project.

Make Excel output as problems on next pages ask.   Follow the order of problems, which makes the project more organized.

After all, following output should be submitted in your Excel file:

• t-test with unequal variances (use data in Project data file worksheet “A. 2020 Putt per Round vs. 2010 Putt per Round”) (20 points)
• Descriptive Statistics (use data “club head speed” in Project data file worksheet B. Drive… ”) (10 pts)
• Descriptive Statistics (use data “driving distance” in data worksheet “B. Drive …”) (10 pts)
• Scatter plot (use data “club head speed” and “driving distance” in data worksheet B.) (10 pts)
• Scatter plot (use data “club head speed” and “driving accuracy” in data worksheet B.) (10 pts)
• Correlation Coefficient (club head speed vs. driving distance) (5 pts)
• Correlation Coefficient (club head speed vs. driving accuracy) (5 pts)
• Regression (use “club head speed” and “driving distance” in data file worksheet B.) (20 pts)

                                                                                      Total 90 points from Excel output

For possible max points for your written answers, refer to each question.    Total 110 points from written answers.                                                                              Project Grand Total 200 points

                                                                                    +Extra credit problems 5pts x2Q’s =10 pts.

Project Problems

Excel file contains data about professional golfers’ performance information.  There are two worksheets (check the tabs at lowest part of the Excel data file):

A. 2020 Putts per Round vs. 2010 Putts per Round

B. Driving- 2020 PGA Tour Championship

With Data in Excel Worksheet “A. 2020 Putts per Round vs. 2010…”

Less putts are better.  We are going to compare recent top performance with that of 10 years ago in golf putting.  It seems that 2020 top 25 players perform slightly better than 2010 top 25 players.  Is it statistically significant?  Through hypothesis testing, let’s check if 2020 top players performed better than 2010 top players. Populations are assumed to be normal and population variances are assumed to be unequal.

Q_A.1. (10 points) Formulate hypotheses for this study question. 

              H₀:

              H_α:

  Specify the year (2020 or 2010) you used for population 1 and for population 2. 

Q_A.2. (5 pts) What is the type of test:  One (left) -tail, One (right) tail, or two-tail test?

 

Q_A.3. (5 pts) We are going to test hypothesis at the significance level 0.05 (α=0.05).  Then, what is the critical value of the test statistic for this hypothesis test?

 

Using data in columns B and E (Players names in column A and D are just to satisfy your curiosity), run “t-test with unequal variances” in Data Analysis of Excel.

Q_A.4.  (5 pts) Review your Excel output.  What is the correct test statistic for this test?

 

Q_A.5.  (10 pts) Using decision rule of test-statistic (classical) method, make your decision and interpret your decision in the context of this test.

With Data in Excel Worksheet “B. Driving- 2020 PGA Tour Championship”

The data set in this worksheet is 2020 performance information of 79 PGA Tour Championship players.  This tournament was randomly chosen out of numerous world-famous professional tournaments.  Data you will use are the three columns of “club head speed”, “driving distance’, and ‘driving accuracy”.  Other columns (names and 2021 data) are just to satisfy your curiosity. 

The significance level for any statistical test, if any, is 0.05 (i.e. α=0.05).

Run “Descriptive Statistics” in Excel on ‘Club Head Speed” and “Driving Distance”. One table for each characteristic.  Some of measures in the output table are beyond this course’s scope.  Check and use the measures we learned in this course.

Q_B.1. Review your descriptive statistics tables and describe (range, center of data, dispersion, distribution) your data. 

• (10 pts) Club Head Speed:

 

 

• (10 pts) Driving Distance:

 

Q_B.2.  (5 pts) With information from Descriptive Statistics” table, figure out 95% confidence interval of True value of Driving Distance of professional top male golfers.  Interpret the interval. 

 

Let’s describe the relation between two characteristics.  Run Excel Scatter Plot and Correlation for following pair of characteristics.

Q_B.3. (10 pts) To verify common sense (faster ball flies farther), check the relation between “Club Head Speed” and “Driving Distance” with Excel Scatter Plot and Correlation Coefficient.  Using proper statistical terms, explain the relation between Club Head Speed and Driving Distance.

 

 

Q_B.4.  (10 pts) Check the relation between “Club Head Speed” and “Driving Accuracy %” with Excel Scatter Plot and Correlation Coefficient.  Using proper statistical terms, explain the relation between “Club Head Speed” and “Driving Accuracy %”.

 

Have you observed approximately linear pattern from the scatter plots?  Let’s check more details on the relation.  Using this data, consider the equation of the regression line,

yˆ=b₀+b₁x, for predicting the Driving Distance based on Club Head Speed.

Double check which (driving distance vs. club head speed) is X, which is Y.  Critical!

(Assumptions about error term in simple linear regression are known to be satisfied). 

Run Excel “regression” to predict Driving Distance based on Club Head Speed. Review output and answer following questions.

Q_B.5.  (5 pts) Find the estimated y-intercept and estimated slope.  Round your answer to three decimal places.

• y-intercept:
• slope:

Q_B.6. (5 pts) Write down the equation of the regression line, using the values in questions Q_B.4 and Q_B. 5. 

 

Q_B.7. (5 pts) Is following statement TRUE or FALSE?  Answer and explain reason.

                           "Not all points predicted by the linear model fall on the same line". 

 

Q_B.8.  (5 pts) According to the estimated linear model, when the club head speed is increased by one mile per hour, what happens to the estimated driver distance?

 

 

Q_B.9. (5 pts) Find the estimated driving distance when a player’s club head speed is 110.00. Round your answer to three decimal places.

 

 

Q_B.10. (5 pts) Find the value of the coefficient of determination. Round your answer to three decimal places.  Interpret the value. 

 

 

 

 

Q_B.11. (for extra credit 5 pts) Let’s say there is a player who just started practicing and his club head speed is 85 mph.  Would it be reasonable to predict his driving distance using the regression model you figured out above? Why or why not?

Q_B.12.  (for extra credit 5 pts) What is (are) the possible limit(s) of this simple linear regression analysis in predicting Driving Distance?  State in no more than 200 words.