The vault apparatus is a commonly shared event between the Women's and Men's Artistic Gymnastics programs. Gymnasts competing in the Vault Apparatus Finals are interested to know if there is evidence to suggest that their score will improve from the vault event of the preceding Individual All-Around Finals. Consider the 2007, 2011, and 2015 gymnasts who competed in both the Individual All-Around Finals and in the Vault Apparatus Finals as sample data. Details of their scores can be found in the Excel sheet "Individual and Vault Apparatus". a) Consider the differences in vault scores between the Apparatus Finals and the Individual All-Around Fina's. (Hint: The sample data are matched pairs. Explain why.) Find the sample mean and sample standard deviation for the differences. b) Estimate, with 90% confidence, the population mean difference in vault scores between the Apparatus Finals and the Individual All-Around. (Hint: Use the results of a) to construct a confidence interval estimate using the t-distribution.) c) Interpret the result in part b) and determine whether there is a difference in vault scores between the two events. Provide a possible explanation for the difference you did or did not observe. Coaches are interested to know if there is a linear relationship between a gymnast's individual score in the Team Competition and their final score in the Individual All- Around Finals. Consider the 2015 male gymnasts as a sample of all male gymnasts. Details of their scores can be found in the Excel sheet "2015 Male Team and Individual". Part A: Regression Analysis on Full Data i. Construct a scatter plot of the Individual All-Around Finals score (dependent) and the individual score in the Team Competition (independent). ii. Find and interpret the correlation coefficient. iii. Find and interpret the coefficient of determination. iv. Find the equation of the trend line and add it to the scatter plot. Part B: Regression Analysis with Observation Removed There is a gymnast who obtained an individual score of 74.035 in the Team Competition and a final score of 40.05 in the Individual All-Around Finals. This observation is an "unusual observation". i. To determine the effect the "unusual observation" has on the relationship between the variables, delete it from your worksheet. After the data point is removed, a. construct a new scatter plot, b. find and interpret the new correlation coefficient, c. find and interpret the new coefficient of determination, d. find the equation of the trend line and add it to the scatter plot, and e. compare the results of b. and c. to ii. and iii. in Part A. ii. Based on your analysis, would you consider the deleted point to be an outlier, influential point, or both? Justify your choice. (Hint: Refer to the information about outliers and influential points provided below.) How to Determine Outlier Influential Point Description An outlier is a point lying far away from other data points. An influential point is a point that strongly affects the equation of the trend line. Examine the scatter plot to see if there is a point that lies outside the pattern of the other points. Obtain the trend line resulting from the data with the point included. Obtain the trend line resulting from the data with the point excluded. Compare to see if the position of the trend line changes significantly. iii. Closely examine the scores obtained in each apparatus event in the Team Competition and Individual All-Around Finals for the gymnast associated with the deleted point. Do you believe it is reasonable to eliminate this gymnast's scores from the analysis? Explain. Part C: Prediction i. Based on your analysis, which trend line equation do you think would give the better prediction for the final score in an Individual All-Around Finals: o the trend line equation using the full data in Part A, or o the trend line equation with the observation removed in Part B? Justify your choice. ii. Using the trend line equation you selected in part i., predict the final score for a male gymnast in the Individual All-Around Finals if he received an individual score of 60.0 in the Team Competition. of 60.0 in the Team 2 3 4 S 6 9 10 11 12 13 14 15 16 17 18 19 20 22 23 A1 24 25 H Upation Data (1 File Home Insert Page Layout Formulas X th D AutoSave Unde A Club B Games Gundur 2015 Fomalo 2015 Female 2015 Female 2015 Fomalo 2015 Female 2015 Female 2015 Female 2015 Female 2015 Female 2011 Female 2011 Female 2011 Female 2011 Female 2011 Fomalo 2011 Fomale 2011 Female 2011 Female 2007 Fomalo 2007 Female 2007 Female 2007 Fomale 2007 Female 2007 Female 27 28 Games 2007 Femalo 2007 Female Arial BIUBB - 10 First Name Fort fx Gymnast information D Gymnast Information Mogan Shalon Rose Last Name Roberts Olsen Woo Brown Shaolyn Sam Molly Laurie Donelo Itzia Briannah Mikaola Emma Kale Anne-Sophie Elaine Sydney Paula Marie Krishna Dominique Hannah Karina Chan Potvin Alycia Maria Marion Amanda Jaclyn Fullor Catherine Dion Mogan Jennifer Halback Jessica Borges Oswald Denommee Podrick Roman Tsang Gerber Sibson Cukassy Kulczyk McEachern Miller Yemany Pegg Swift -A A 1. A- MacCallum Data Review View Help . PT Age ON BC QC AB ON MB QC SK BC BC ON BC QC OC MB NS ON ON BC BC QC ON SK NB 14 14 15 Vaut 14 18 17 N/A 14 N/A 16 17 N/A N/A G N/A 15 15.15 14.4 14.2 14.3 14.05 13.75 144 14.1 13.15 13.4 13.7 13.55 14.45 15.05 15.15 15 14.5 14.8 Alignment 13.65 Uneven Bars NA N/A N/A N/A H N/A 14.5 14.55 15.4 11.5 13.85 11.2 O Search (Alt+Q) Wrap Text Merge & Center N/A N/A 407 13.3 12.3 12.05 13.3 12.65 NA 12.4 N/A 13.65 14.1 14.75 13.6 12.5 NA K Individual All-Around Finals Final Floor Score N/A N/A 12.25 12.95 13.8 13.25 13.1 13.55 14.8 15.06 15.2 14.85 15 N/A LISE 14.05 13.7 NA 13.4 General 14 65 14.1 15.35 14.3 $%988 14.75 13.65 N/A 12.1 9.9 13.55 48.95 10.05 112 12:3 13.9 12.85 12.55 13.65 15.3 13.35 12:25 12.8 14:4 13.2 14:35 12.55 14:35 13.1 14.25 N/A N/A N/A Number N/A 58,35 58.65 59.55 53.35 54.35 52.55 53.1 53.7 54 85 50.15 47.25 52 85 58.05 54.75 57.7 56 85 NA 13.8 55.05 L N/A N/A Rank 50.15 55.8 N/A NA N/A 37118 2 1113 16 14 7 10 12:55 Pommet Horse Rings Para Horizontal Bors Bar PT Age Floor Vaut First Name Jeremit Last Namo Faithualamenny OAL NUK M Gender Female Apparatus Male Team Male Individual All Around Male Apparatus Individual and Vault Apparatus AT 45.BC * 494 * 14 18 22 8 1 11 3 5 6 7 Conditional Format as Cell Formatting Table Styles styles M N P Vault Apparatus Finals Rank Final Score 15.35 15.3 14.85 14.5 14 35 14:25 14.2 14.1 14 14.45 13.9 13.85 13.65 136 13.55 13.5 13.5 15.4 15.2 15.05 14.95 Insect Delete Format 14.85 14.85 14.6 13.95 Final Scom 10.604 Team Medal and Apparatus Final Score ALLE 2 3 4 5 6 7 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 Q Rank 2015 Male Team & 2 3 5 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 A1 24 25 27 C File Unde AutoSave H Upmatic Data (1) Home Insert Page Layout Formulas Data Review X t UP A Games Tome Club B Gunder 2015 Fomalo 2015 Female 2015 Female 2015 Fomalo 2015 Female 2015 Female 2015 Female 2015 Female 2015 Female 2011 Female 2011 Femalo 2011 Female 2011 Female 2011 Fomalo 2011 Fomalo 2011 Female 2011 Female 2007 Fomalo 2007 Female 2007 Female 2007 Fomale 2007 Female 2007 Female 2007 Femalo 2007 Female Anal - 10 BIU - Font Xfx Gymnast Information D Gymnast Information First Name Mogan Shallon Rose Shaolyn Sam Molly Laurie Donello Itzia Briannah Mikaola Emma Kale Anne-Sophie Elano Sydney Paula Marie Krishna Dominique Hannah Karina Alycia Maria Chan Marion Potvin Amanda Jaclyn Fuller Dian Catherine Mogan Jennifer Halback Jessica Last Name Roberts Olson Woo Brown Borges Oswald -A A &-A- Denommee Podnick Roman Tsang Gerber Sibson Csukassy Kulczyk McEachern Miler Yemany Pegg Swift MacCallum PT Last Namo ON BC QC AB ON MB QC SK BC BC ON BC QC OC MB NS ON ON BC BC QC ON QC SK NB View Help . Age Vaut 14 14 15 14 18 17 N/A 14 N/A 16 17 N/A N/A G N/A 15 15 15 14.4 14.2 14.3 14.05 13.75 14.4 14.1 13.15 13.4 13.7 13.55 14.45 Alignment 15 14.5 148 Uneven Bars N/A N/A H 14.5 14.55 15.4 11.5 N/A 13.85 11.2 O Search (Alt-08 Wrap Text Merge & Center 407 Beam N/A N/A 13.3 12.3 12.65 13.3 12.65 N/A NA N/A 12.4 N/A N/A 12.1 10.05 13.9 13.65 15.05 13.35 12:25 15.15 12.8 14.4 13.2 14.35 12.55 13.1 K Individual All-Around Finals Final Scom Rank 13.65 14.1 14.75 13.6 12.5 NA Floor N/A N/A 12.25 13.8 13.1 13.55 15.05 N/A 152 58,35 14.85 58.65 15 59.55 14.05 53.35 13.7 54.35 12.95 13.25 General $ % 98 48 52.55 53.1 53.7 14.8 54 85 N/A 13.4 50.15 NA 99 13.55 48.95 112 12:3 47.25 12.85 12.55 52 85 15.3 14.65 58.05 14.1 54.75 15.35 57.7 56 85 14.3 14:35 14.75 56.15 14.25 13.65 55.8 NA N/A 13.8 Vaut Number N/A NA L N/A NA N/A NA N/A 32118 1113 16 14 13.65 12:55 10 Pommal Horse 5505 Parall Horizontal Bors Bar Games NUE Hz. PT Age Floor Gender First Name Rings Female Apparatus Male Team Male Individual All Around Male Apparatus Individual and Vault Apparatus Jeremi Balkalomma CAL 43 45.BC LISE FEDE 494 40 7 14 18 22 8 1 11 3 5 6 7 Conditional Format as Cell Formatting Table Styles Styles M Final Scom N P Vault Apparatus Finals Rank Final Score 15.35 15.3 14.85 14:5 1435 14 25 14.2 14/1 14 14.45 13.9 13.85 13.65 Insert Delete Format 136 13.55 13.5 13.5 15.4 15.2 15.05 14.95 14.85 14 85 14.6 13.95 10.EDA Final Score Team Medal and Apparatus LLEE 1 2 3 4 5 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 Q Rank 2015 Male Team & The vault apparatus is a commonly shared event between the Women's and Men's Artistic Gymnastics programs. Gymnasts competing in the Vault Apparatus Finals are interested to know if there is evidence to suggest that their score will improve from the vault event of the preceding Individual All-Around Finals. Consider the 2007, 2011, and 2015 gymnasts who competed in both the Individual All-Around Finals and in the Vault Apparatus Finals as sample data. Details of their scores can be found in the Excel sheet "Individual and Vault Apparatus". a) Consider the differences in vault scores between the Apparatus Finals and the Individual All-Around Fina's. (Hint: The sample data are matched pairs. Explain why.) Find the sample mean and sample standard deviation for the differences. b) Estimate, with 90% confidence, the population mean difference in vault scores between the Apparatus Finals and the Individual All-Around. (Hint: Use the results of a) to construct a confidence interval estimate using the t-distribution.) c) Interpret the result in part b) and determine whether there is a difference in vault scores between the two events. Provide a possible explanation for the difference you did or did not observe. Coaches are interested to know if there is a linear relationship between a gymnast's individual score in the Team Competition and their final score in the Individual All- Around Finals. Consider the 2015 male gymnasts as a sample of all male gymnasts. Details of their scores can be found in the Excel sheet "2015 Male Team and Individual". Part A: Regression Analysis on Full Data i. Construct a scatter plot of the Individual All-Around Finals score (dependent) and the individual score in the Team Competition (independent). ii. Find and interpret the correlation coefficient. iii. Find and interpret the coefficient of determination. iv. Find the equation of the trend line and add it to the scatter plot. Part B: Regression Analysis with Observation Removed There is a gymnast who obtained an individual score of 74.035 in the Team Competition and a final score of 40.05 in the Individual All-Around Finals. This observation is an "unusual observation". i. To determine the effect the "unusual observation" has on the relationship between the variables, delete it from your worksheet. After the data point is removed, a. construct a new scatter plot, b. find and interpret the new correlation coefficient, c. find and interpret the new coefficient of determination, d. find the equation of the trend line and add it to the scatter plot, and e. compare the results of b. and c. to ii. and iii. in Part A. ii. Based on your analysis, would you consider the deleted point to be an outlier, influential point, or both? Justify your choice. (Hint: Refer to the information about outliers and influential points provided below.) How to Determine Outlier Influential Point Description An outlier is a point lying far away from other data points. An influential point is a point that strongly affects the equation of the trend line. Examine the scatter plot to see if there is a point that lies outside the pattern of the other points. Obtain the trend line resulting from the data with the point included. Obtain the trend line resulting from the data with the point excluded. Compare to see if the position of the trend line changes significantly. iii. Closely examine the scores obtained in each apparatus event in the Team Competition and Individual All-Around Finals for the gymnast associated with the deleted point. Do you believe it is reasonable to eliminate this gymnast's scores from the analysis? Explain. Part C: Prediction i. Based on your analysis, which trend line equation do you think would give the better prediction for the final score in an Individual All-Around Finals: o the trend line equation using the full data in Part A, or o the trend line equation with the observation removed in Part B? Justify your choice. ii. Using the trend line equation you selected in part i., predict the final score for a male gymnast in the Individual All-Around Finals if he received an individual score of 60.0 in the Team Competition. of 60.0 in the Team 2 3 4 S 6 9 10 11 12 13 14 15 16 17 18 19 20 22 23 A1 24 25 H Upation Data (1 File Home Insert Page Layout Formulas X th D AutoSave Unde A Club B Games Gundur 2015 Fomalo 2015 Female 2015 Female 2015 Fomalo 2015 Female 2015 Female 2015 Female 2015 Female 2015 Female 2011 Female 2011 Female 2011 Female 2011 Female 2011 Fomalo 2011 Fomale 2011 Female 2011 Female 2007 Fomalo 2007 Female 2007 Female 2007 Fomale 2007 Female 2007 Female 27 28 Games 2007 Femalo 2007 Female Arial BIUBB - 10 First Name Fort fx Gymnast information D Gymnast Information Mogan Shalon Rose Last Name Roberts Olsen Woo Brown Shaolyn Sam Molly Laurie Donelo Itzia Briannah Mikaola Emma Kale Anne-Sophie Elaine Sydney Paula Marie Krishna Dominique Hannah Karina Chan Potvin Alycia Maria Marion Amanda Jaclyn Fullor Catherine Dion Mogan Jennifer Halback Jessica Borges Oswald Denommee Podrick Roman Tsang Gerber Sibson Cukassy Kulczyk McEachern Miller Yemany Pegg Swift -A A 1. A- MacCallum Data Review View Help . PT Age ON BC QC AB ON MB QC SK BC BC ON BC QC OC MB NS ON ON BC BC QC ON SK NB 14 14 15 Vaut 14 18 17 N/A 14 N/A 16 17 N/A N/A G N/A 15 15.15 14.4 14.2 14.3 14.05 13.75 144 14.1 13.15 13.4 13.7 13.55 14.45 15.05 15.15 15 14.5 14.8 Alignment 13.65 Uneven Bars NA N/A N/A N/A H N/A 14.5 14.55 15.4 11.5 13.85 11.2 O Search (Alt+Q) Wrap Text Merge & Center N/A N/A 407 13.3 12.3 12.05 13.3 12.65 NA 12.4 N/A 13.65 14.1 14.75 13.6 12.5 NA K Individual All-Around Finals Final Floor Score N/A N/A 12.25 12.95 13.8 13.25 13.1 13.55 14.8 15.06 15.2 14.85 15 N/A LISE 14.05 13.7 NA 13.4 General 14 65 14.1 15.35 14.3 $%988 14.75 13.65 N/A 12.1 9.9 13.55 48.95 10.05 112 12:3 13.9 12.85 12.55 13.65 15.3 13.35 12:25 12.8 14:4 13.2 14:35 12.55 14:35 13.1 14.25 N/A N/A N/A Number N/A 58,35 58.65 59.55 53.35 54.35 52.55 53.1 53.7 54 85 50.15 47.25 52 85 58.05 54.75 57.7 56 85 NA 13.8 55.05 L N/A N/A Rank 50.15 55.8 N/A NA N/A 37118 2 1113 16 14 7 10 12:55 Pommet Horse Rings Para Horizontal Bors Bar PT Age Floor Vaut First Name Jeremit Last Namo Faithualamenny OAL NUK M Gender Female Apparatus Male Team Male Individual All Around Male Apparatus Individual and Vault Apparatus AT 45.BC * 494 * 14 18 22 8 1 11 3 5 6 7 Conditional Format as Cell Formatting Table Styles styles M N P Vault Apparatus Finals Rank Final Score 15.35 15.3 14.85 14.5 14 35 14:25 14.2 14.1 14 14.45 13.9 13.85 13.65 136 13.55 13.5 13.5 15.4 15.2 15.05 14.95 Insect Delete Format 14.85 14.85 14.6 13.95 Final Scom 10.604 Team Medal and Apparatus Final Score ALLE 2 3 4 5 6 7 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 Q Rank 2015 Male Team & 2 3 5 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 A1 24 25 27 C File Unde AutoSave H Upmatic Data (1) Home Insert Page Layout Formulas Data Review X t UP A Games Tome Club B Gunder 2015 Fomalo 2015 Female 2015 Female 2015 Fomalo 2015 Female 2015 Female 2015 Female 2015 Female 2015 Female 2011 Female 2011 Femalo 2011 Female 2011 Female 2011 Fomalo 2011 Fomalo 2011 Female 2011 Female 2007 Fomalo 2007 Female 2007 Female 2007 Fomale 2007 Female 2007 Female 2007 Femalo 2007 Female Anal - 10 BIU - Font Xfx Gymnast Information D Gymnast Information First Name Mogan Shallon Rose Shaolyn Sam Molly Laurie Donello Itzia Briannah Mikaola Emma Kale Anne-Sophie Elano Sydney Paula Marie Krishna Dominique Hannah Karina Alycia Maria Chan Marion Potvin Amanda Jaclyn Fuller Dian Catherine Mogan Jennifer Halback Jessica Last Name Roberts Olson Woo Brown Borges Oswald -A A &-A- Denommee Podnick Roman Tsang Gerber Sibson Csukassy Kulczyk McEachern Miler Yemany Pegg Swift MacCallum PT Last Namo ON BC QC AB ON MB QC SK BC BC ON BC QC OC MB NS ON ON BC BC QC ON QC SK NB View Help . Age Vaut 14 14 15 14 18 17 N/A 14 N/A 16 17 N/A N/A G N/A 15 15 15 14.4 14.2 14.3 14.05 13.75 14.4 14.1 13.15 13.4 13.7 13.55 14.45 Alignment 15 14.5 148 Uneven Bars N/A N/A H 14.5 14.55 15.4 11.5 N/A 13.85 11.2 O Search (Alt-08 Wrap Text Merge & Center 407 Beam N/A N/A 13.3 12.3 12.65 13.3 12.65 N/A NA N/A 12.4 N/A N/A 12.1 10.05 13.9 13.65 15.05 13.35 12:25 15.15 12.8 14.4 13.2 14.35 12.55 13.1 K Individual All-Around Finals Final Scom Rank 13.65 14.1 14.75 13.6 12.5 NA Floor N/A N/A 12.25 13.8 13.1 13.55 15.05 N/A 152 58,35 14.85 58.65 15 59.55 14.05 53.35 13.7 54.35 12.95 13.25 General $ % 98 48 52.55 53.1 53.7 14.8 54 85 N/A 13.4 50.15 NA 99 13.55 48.95 112 12:3 47.25 12.85 12.55 52 85 15.3 14.65 58.05 14.1 54.75 15.35 57.7 56 85 14.3 14:35 14.75 56.15 14.25 13.65 55.8 NA N/A 13.8 Vaut Number N/A NA L N/A NA N/A NA N/A 32118 1113 16 14 13.65 12:55 10 Pommal Horse 5505 Parall Horizontal Bors Bar Games NUE Hz. PT Age Floor Gender First Name Rings Female Apparatus Male Team Male Individual All Around Male Apparatus Individual and Vault Apparatus Jeremi Balkalomma CAL 43 45.BC LISE FEDE 494 40 7 14 18 22 8 1 11 3 5 6 7 Conditional Format as Cell Formatting Table Styles Styles M Final Scom N P Vault Apparatus Finals Rank Final Score 15.35 15.3 14.85 14:5 1435 14 25 14.2 14/1 14 14.45 13.9 13.85 13.65 Insert Delete Format 136 13.55 13.5 13.5 15.4 15.2 15.05 14.95 14.85 14 85 14.6 13.95 10.EDA Final Score Team Medal and Apparatus LLEE 1 2 3 4 5 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 Q Rank 2015 Male Team & The vault apparatus is a commonly shared event between the Women's and Men's Artistic Gymnastics programs. Gymnasts competing in the Vault Apparatus Finals are interested to know if there is evidence to suggest that their score will improve from the vault event of the preceding Individual All-Around Finals. Consider the 2007, 2011, and 2015 gymnasts who competed in both the Individual All-Around Finals and in the Vault Apparatus Finals as sample data. Details of their scores can be found in the Excel sheet "Individual and Vault Apparatus". a) Consider the differences in vault scores between the Apparatus Finals and the Individual All-Around Fina's. (Hint: The sample data are matched pairs. Explain why.) Find the sample mean and sample standard deviation for the differences. b) Estimate, with 90% confidence, the population mean difference in vault scores between the Apparatus Finals and the Individual All-Around. (Hint: Use the results of a) to construct a confidence interval estimate using the t-distribution.) c) Interpret the result in part b) and determine whether there is a difference in vault scores between the two events. Provide a possible explanation for the difference you did or did not observe. Coaches are interested to know if there is a linear relationship between a gymnast's individual score in the Team Competition and their final score in the Individual All- Around Finals. Consider the 2015 male gymnasts as a sample of all male gymnasts. Details of their scores can be found in the Excel sheet "2015 Male Team and Individual". Part A: Regression Analysis on Full Data i. Construct a scatter plot of the Individual All-Around Finals score (dependent) and the individual score in the Team Competition (independent). ii. Find and interpret the correlation coefficient. iii. Find and interpret the coefficient of determination. iv. Find the equation of the trend line and add it to the scatter plot. Part B: Regression Analysis with Observation Removed There is a gymnast who obtained an individual score of 74.035 in the Team Competition and a final score of 40.05 in the Individual All-Around Finals. This observation is an "unusual observation". i. To determine the effect the "unusual observation" has on the relationship between the variables, delete it from your worksheet. After the data point is removed, a. construct a new scatter plot, b. find and interpret the new correlation coefficient, c. find and interpret the new coefficient of determination, d. find the equation of the trend line and add it to the scatter plot, and e. compare the results of b. and c. to ii. and iii. in Part A. ii. Based on your analysis, would you consider the deleted point to be an outlier, influential point, or both? Justify your choice. (Hint: Refer to the information about outliers and influential points provided below.) How to Determine Outlier Influential Point Description An outlier is a point lying far away from other data points. An influential point is a point that strongly affects the equation of the trend line. Examine the scatter plot to see if there is a point that lies outside the pattern of the other points. Obtain the trend line resulting from the data with the point included. Obtain the trend line resulting from the data with the point excluded. Compare to see if the position of the trend line changes significantly. iii. Closely examine the scores obtained in each apparatus event in the Team Competition and Individual All-Around Finals for the gymnast associated with the deleted point. Do you believe it is reasonable to eliminate this gymnast's scores from the analysis? Explain. Part C: Prediction i. Based on your analysis, which trend line equation do you think would give the better prediction for the final score in an Individual All-Around Finals: o the trend line equation using the full data in Part A, or o the trend line equation with the observation removed in Part B? Justify your choice. ii. Using the trend line equation you selected in part i., predict the final score for a male gymnast in the Individual All-Around Finals if he received an individual score of 60.0 in the Team Competition. of 60.0 in the Team 2 3 4 S 6 9 10 11 12 13 14 15 16 17 18 19 20 22 23 A1 24 25 H Upation Data (1 File Home Insert Page Layout Formulas X th D AutoSave Unde A Club B Games Gundur 2015 Fomalo 2015 Female 2015 Female 2015 Fomalo 2015 Female 2015 Female 2015 Female 2015 Female 2015 Female 2011 Female 2011 Female 2011 Female 2011 Female 2011 Fomalo 2011 Fomale 2011 Female 2011 Female 2007 Fomalo 2007 Female 2007 Female 2007 Fomale 2007 Female 2007 Female 27 28 Games 2007 Femalo 2007 Female Arial BIUBB - 10 First Name Fort fx Gymnast information D Gymnast Information Mogan Shalon Rose Last Name Roberts Olsen Woo Brown Shaolyn Sam Molly Laurie Donelo Itzia Briannah Mikaola Emma Kale Anne-Sophie Elaine Sydney Paula Marie Krishna Dominique Hannah Karina Chan Potvin Alycia Maria Marion Amanda Jaclyn Fullor Catherine Dion Mogan Jennifer Halback Jessica Borges Oswald Denommee Podrick Roman Tsang Gerber Sibson Cukassy Kulczyk McEachern Miller Yemany Pegg Swift -A A 1. A- MacCallum Data Review View Help . PT Age ON BC QC AB ON MB QC SK BC BC ON BC QC OC MB NS ON ON BC BC QC ON SK NB 14 14 15 Vaut 14 18 17 N/A 14 N/A 16 17 N/A N/A G N/A 15 15.15 14.4 14.2 14.3 14.05 13.75 144 14.1 13.15 13.4 13.7 13.55 14.45 15.05 15.15 15 14.5 14.8 Alignment 13.65 Uneven Bars NA N/A N/A N/A H N/A 14.5 14.55 15.4 11.5 13.85 11.2 O Search (Alt+Q) Wrap Text Merge & Center N/A N/A 407 13.3 12.3 12.05 13.3 12.65 NA 12.4 N/A 13.65 14.1 14.75 13.6 12.5 NA K Individual All-Around Finals Final Floor Score N/A N/A 12.25 12.95 13.8 13.25 13.1 13.55 14.8 15.06 15.2 14.85 15 N/A LISE 14.05 13.7 NA 13.4 General 14 65 14.1 15.35 14.3 $%988 14.75 13.65 N/A 12.1 9.9 13.55 48.95 10.05 112 12:3 13.9 12.85 12.55 13.65 15.3 13.35 12:25 12.8 14:4 13.2 14:35 12.55 14:35 13.1 14.25 N/A N/A N/A Number N/A 58,35 58.65 59.55 53.35 54.35 52.55 53.1 53.7 54 85 50.15 47.25 52 85 58.05 54.75 57.7 56 85 NA 13.8 55.05 L N/A N/A Rank 50.15 55.8 N/A NA N/A 37118 2 1113 16 14 7 10 12:55 Pommet Horse Rings Para Horizontal Bors Bar PT Age Floor Vaut First Name Jeremit Last Namo Faithualamenny OAL NUK M Gender Female Apparatus Male Team Male Individual All Around Male Apparatus Individual and Vault Apparatus AT 45.BC * 494 * 14 18 22 8 1 11 3 5 6 7 Conditional Format as Cell Formatting Table Styles styles M N P Vault Apparatus Finals Rank Final Score 15.35 15.3 14.85 14.5 14 35 14:25 14.2 14.1 14 14.45 13.9 13.85 13.65 136 13.55 13.5 13.5 15.4 15.2 15.05 14.95 Insect Delete Format 14.85 14.85 14.6 13.95 Final Scom 10.604 Team Medal and Apparatus Final Score ALLE 2 3 4 5 6 7 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 Q Rank 2015 Male Team & 2 3 5 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 A1 24 25 27 C File Unde AutoSave H Upmatic Data (1) Home Insert Page Layout Formulas Data Review X t UP A Games Tome Club B Gunder 2015 Fomalo 2015 Female 2015 Female 2015 Fomalo 2015 Female 2015 Female 2015 Female 2015 Female 2015 Female 2011 Female 2011 Femalo 2011 Female 2011 Female 2011 Fomalo 2011 Fomalo 2011 Female 2011 Female 2007 Fomalo 2007 Female 2007 Female 2007 Fomale 2007 Female 2007 Female 2007 Femalo 2007 Female Anal - 10 BIU - Font Xfx Gymnast Information D Gymnast Information First Name Mogan Shallon Rose Shaolyn Sam Molly Laurie Donello Itzia Briannah Mikaola Emma Kale Anne-Sophie Elano Sydney Paula Marie Krishna Dominique Hannah Karina Alycia Maria Chan Marion Potvin Amanda Jaclyn Fuller Dian Catherine Mogan Jennifer Halback Jessica Last Name Roberts Olson Woo Brown Borges Oswald -A A &-A- Denommee Podnick Roman Tsang Gerber Sibson Csukassy Kulczyk McEachern Miler Yemany Pegg Swift MacCallum PT Last Namo ON BC QC AB ON MB QC SK BC BC ON BC QC OC MB NS ON ON BC BC QC ON QC SK NB View Help . Age Vaut 14 14 15 14 18 17 N/A 14 N/A 16 17 N/A N/A G N/A 15 15 15 14.4 14.2 14.3 14.05 13.75 14.4 14.1 13.15 13.4 13.7 13.55 14.45 Alignment 15 14.5 148 Uneven Bars N/A N/A H 14.5 14.55 15.4 11.5 N/A 13.85 11.2 O Search (Alt-08 Wrap Text Merge & Center 407 Beam N/A N/A 13.3 12.3 12.65 13.3 12.65 N/A NA N/A 12.4 N/A N/A 12.1 10.05 13.9 13.65 15.05 13.35 12:25 15.15 12.8 14.4 13.2 14.35 12.55 13.1 K Individual All-Around Finals Final Scom Rank 13.65 14.1 14.75 13.6 12.5 NA Floor N/A N/A 12.25 13.8 13.1 13.55 15.05 N/A 152 58,35 14.85 58.65 15 59.55 14.05 53.35 13.7 54.35 12.95 13.25 General $ % 98 48 52.55 53.1 53.7 14.8 54 85 N/A 13.4 50.15 NA 99 13.55 48.95 112 12:3 47.25 12.85 12.55 52 85 15.3 14.65 58.05 14.1 54.75 15.35 57.7 56 85 14.3 14:35 14.75 56.15 14.25 13.65 55.8 NA N/A 13.8 Vaut Number N/A NA L N/A NA N/A NA N/A 32118 1113 16 14 13.65 12:55 10 Pommal Horse 5505 Parall Horizontal Bors Bar Games NUE Hz. PT Age Floor Gender First Name Rings Female Apparatus Male Team Male Individual All Around Male Apparatus Individual and Vault Apparatus Jeremi Balkalomma CAL 43 45.BC LISE FEDE 494 40 7 14 18 22 8 1 11 3 5 6 7 Conditional Format as Cell Formatting Table Styles Styles M Final Scom N P Vault Apparatus Finals Rank Final Score 15.35 15.3 14.85 14:5 1435 14 25 14.2 14/1 14 14.45 13.9 13.85 13.65 Insert Delete Format 136 13.55 13.5 13.5 15.4 15.2 15.05 14.95 14.85 14 85 14.6 13.95 10.EDA Final Score Team Medal and Apparatus LLEE 1 2 3 4 5 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 Q Rank 2015 Male Team & The vault apparatus is a commonly shared event between the Women's and Men's Artistic Gymnastics programs. Gymnasts competing in the Vault Apparatus Finals are interested to know if there is evidence to suggest that their score will improve from the vault event of the preceding Individual All-Around Finals. Consider the 2007, 2011, and 2015 gymnasts who competed in both the Individual All-Around Finals and in the Vault Apparatus Finals as sample data. Details of their scores can be found in the Excel sheet "Individual and Vault Apparatus". a) Consider the differences in vault scores between the Apparatus Finals and the Individual All-Around Fina's. (Hint: The sample data are matched pairs. Explain why.) Find the sample mean and sample standard deviation for the differences. b) Estimate, with 90% confidence, the population mean difference in vault scores between the Apparatus Finals and the Individual All-Around. (Hint: Use the results of a) to construct a confidence interval estimate using the t-distribution.) c) Interpret the result in part b) and determine whether there is a difference in vault scores between the two events. Provide a possible explanation for the difference you did or did not observe. Coaches are interested to know if there is a linear relationship between a gymnast's individual score in the Team Competition and their final score in the Individual All- Around Finals. Consider the 2015 male gymnasts as a sample of all male gymnasts. Details of their scores can be found in the Excel sheet "2015 Male Team and Individual". Part A: Regression Analysis on Full Data i. Construct a scatter plot of the Individual All-Around Finals score (dependent) and the individual score in the Team Competition (independent). ii. Find and interpret the correlation coefficient. iii. Find and interpret the coefficient of determination. iv. Find the equation of the trend line and add it to the scatter plot. Part B: Regression Analysis with Observation Removed There is a gymnast who obtained an individual score of 74.035 in the Team Competition and a final score of 40.05 in the Individual All-Around Finals. This observation is an "unusual observation". i. To determine the effect the "unusual observation" has on the relationship between the variables, delete it from your worksheet. After the data point is removed, a. construct a new scatter plot, b. find and interpret the new correlation coefficient, c. find and interpret the new coefficient of determination, d. find the equation of the trend line and add it to the scatter plot, and e. compare the results of b. and c. to ii. and iii. in Part A. ii. Based on your analysis, would you consider the deleted point to be an outlier, influential point, or both? Justify your choice. (Hint: Refer to the information about outliers and influential points provided below.) How to Determine Outlier Influential Point Description An outlier is a point lying far away from other data points. An influential point is a point that strongly affects the equation of the trend line. Examine the scatter plot to see if there is a point that lies outside the pattern of the other points. Obtain the trend line resulting from the data with the point included. Obtain the trend line resulting from the data with the point excluded. Compare to see if the position of the trend line changes significantly. iii. Closely examine the scores obtained in each apparatus event in the Team Competition and Individual All-Around Finals for the gymnast associated with the deleted point. Do you believe it is reasonable to eliminate this gymnast's scores from the analysis? Explain. Part C: Prediction i. Based on your analysis, which trend line equation do you think would give the better prediction for the final score in an Individual All-Around Finals: o the trend line equation using the full data in Part A, or o the trend line equation with the observation removed in Part B? Justify your choice. ii. Using the trend line equation you selected in part i., predict the final score for a male gymnast in the Individual All-Around Finals if he received an individual score of 60.0 in the Team Competition. of 60.0 in the Team 2 3 4 S 6 9 10 11 12 13 14 15 16 17 18 19 20 22 23 A1 24 25 H Upation Data (1 File Home Insert Page Layout Formulas X th D AutoSave Unde A Club B Games Gundur 2015 Fomalo 2015 Female 2015 Female 2015 Fomalo 2015 Female 2015 Female 2015 Female 2015 Female 2015 Female 2011 Female 2011 Female 2011 Female 2011 Female 2011 Fomalo 2011 Fomale 2011 Female 2011 Female 2007 Fomalo 2007 Female 2007 Female 2007 Fomale 2007 Female 2007 Female 27 28 Games 2007 Femalo 2007 Female Arial BIUBB - 10 First Name Fort fx Gymnast information D Gymnast Information Mogan Shalon Rose Last Name Roberts Olsen Woo Brown Shaolyn Sam Molly Laurie Donelo Itzia Briannah Mikaola Emma Kale Anne-Sophie Elaine Sydney Paula Marie Krishna Dominique Hannah Karina Chan Potvin Alycia Maria Marion Amanda Jaclyn Fullor Catherine Dion Mogan Jennifer Halback Jessica Borges Oswald Denommee Podrick Roman Tsang Gerber Sibson Cukassy Kulczyk McEachern Miller Yemany Pegg Swift -A A 1. A- MacCallum Data Review View Help . PT Age ON BC QC AB ON MB QC SK BC BC ON BC QC OC MB NS ON ON BC BC QC ON SK NB 14 14 15 Vaut 14 18 17 N/A 14 N/A 16 17 N/A N/A G N/A 15 15.15 14.4 14.2 14.3 14.05 13.75 144 14.1 13.15 13.4 13.7 13.55 14.45 15.05 15.15 15 14.5 14.8 Alignment 13.65 Uneven Bars NA N/A N/A N/A H N/A 14.5 14.55 15.4 11.5 13.85 11.2 O Search (Alt+Q) Wrap Text Merge & Center N/A N/A 407 13.3 12.3 12.05 13.3 12.65 NA 12.4 N/A 13.65 14.1 14.75 13.6 12.5 NA K Individual All-Around Finals Final Floor Score N/A N/A 12.25 12.95 13.8 13.25 13.1 13.55 14.8 15.06 15.2 14.85 15 N/A LISE 14.05 13.7 NA 13.4 General 14 65 14.1 15.35 14.3 $%988 14.75 13.65 N/A 12.1 9.9 13.55 48.95 10.05 112 12:3 13.9 12.85 12.55 13.65 15.3 13.35 12:25 12.8 14:4 13.2 14:35 12.55 14:35 13.1 14.25 N/A N/A N/A Number N/A 58,35 58.65 59.55 53.35 54.35 52.55 53.1 53.7 54 85 50.15 47.25 52 85 58.05 54.75 57.7 56 85 NA 13.8 55.05 L N/A N/A Rank 50.15 55.8 N/A NA N/A 37118 2 1113 16 14 7 10 12:55 Pommet Horse Rings Para Horizontal Bors Bar PT Age Floor Vaut First Name Jeremit Last Namo Faithualamenny OAL NUK M Gender Female Apparatus Male Team Male Individual All Around Male Apparatus Individual and Vault Apparatus AT 45.BC * 494 * 14 18 22 8 1 11 3 5 6 7 Conditional Format as Cell Formatting Table Styles styles M N P Vault Apparatus Finals Rank Final Score 15.35 15.3 14.85 14.5 14 35 14:25 14.2 14.1 14 14.45 13.9 13.85 13.65 136 13.55 13.5 13.5 15.4 15.2 15.05 14.95 Insect Delete Format 14.85 14.85 14.6 13.95 Final Scom 10.604 Team Medal and Apparatus Final Score ALLE 2 3 4 5 6 7 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 Q Rank 2015 Male Team & 2 3 5 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 A1 24 25 27 C File Unde AutoSave H Upmatic Data (1) Home Insert Page Layout Formulas Data Review X t UP A Games Tome Club B Gunder 2015 Fomalo 2015 Female 2015 Female 2015 Fomalo 2015 Female 2015 Female 2015 Female 2015 Female 2015 Female 2011 Female 2011 Femalo 2011 Female 2011 Female 2011 Fomalo 2011 Fomalo 2011 Female 2011 Female 2007 Fomalo 2007 Female 2007 Female 2007 Fomale 2007 Female 2007 Female 2007 Femalo 2007 Female Anal - 10 BIU - Font Xfx Gymnast Information D Gymnast Information First Name Mogan Shallon Rose Shaolyn Sam Molly Laurie Donello Itzia Briannah Mikaola Emma Kale Anne-Sophie Elano Sydney Paula Marie Krishna Dominique Hannah Karina Alycia Maria Chan Marion Potvin Amanda Jaclyn Fuller Dian Catherine Mogan Jennifer Halback Jessica Last Name Roberts Olson Woo Brown Borges Oswald -A A &-A- Denommee Podnick Roman Tsang Gerber Sibson Csukassy Kulczyk McEachern Miler Yemany Pegg Swift MacCallum PT Last Namo ON BC QC AB ON MB QC SK BC BC ON BC QC OC MB NS ON ON BC BC QC ON QC SK NB View Help . Age Vaut 14 14 15 14 18 17 N/A 14 N/A 16 17 N/A N/A G N/A 15 15 15 14.4 14.2 14.3 14.05 13.75 14.4 14.1 13.15 13.4 13.7 13.55 14.45 Alignment 15 14.5 148 Uneven Bars N/A N/A H 14.5 14.55 15.4 11.5 N/A 13.85 11.2 O Search (Alt-08 Wrap Text Merge & Center 407 Beam N/A N/A 13.3 12.3 12.65 13.3 12.65 N/A NA N/A 12.4 N/A N/A 12.1 10.05 13.9 13.65 15.05 13.35 12:25 15.15 12.8 14.4 13.2 14.35 12.55 13.1 K Individual All-Around Finals Final Scom Rank 13.65 14.1 14.75 13.6 12.5 NA Floor N/A N/A 12.25 13.8 13.1 13.55 15.05 N/A 152 58,35 14.85 58.65 15 59.55 14.05 53.35 13.7 54.35 12.95 13.25 General $ % 98 48 52.55 53.1 53.7 14.8 54 85 N/A 13.4 50.15 NA 99 13.55 48.95 112 12:3 47.25 12.85 12.55 52 85 15.3 14.65 58.05 14.1 54.75 15.35 57.7 56 85 14.3 14:35 14.75 56.15 14.25 13.65 55.8 NA N/A 13.8 Vaut Number N/A NA L N/A NA N/A NA N/A 32118 1113 16 14 13.65 12:55 10 Pommal Horse 5505 Parall Horizontal Bors Bar Games NUE Hz. PT Age Floor Gender First Name Rings Female Apparatus Male Team Male Individual All Around Male Apparatus Individual and Vault Apparatus Jeremi Balkalomma CAL 43 45.BC LISE FEDE 494 40 7 14 18 22 8 1 11 3 5 6 7 Conditional Format as Cell Formatting Table Styles Styles M Final Scom N P Vault Apparatus Finals Rank Final Score 15.35 15.3 14.85 14:5 1435 14 25 14.2 14/1 14 14.45 13.9 13.85 13.65 Insert Delete Format 136 13.55 13.5 13.5 15.4 15.2 15.05 14.95 14.85 14 85 14.6 13.95 10.EDA Final Score Team Medal and Apparatus LLEE 1 2 3 4 5 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 Q Rank 2015 Male Team &