MATH 1040 Group 2 Term Project Presentation Design

MATH 1040 Group 2 Term Project Presentation Design & Purpose of the Study Design Data Statistics, & Graphs Difficulties & Surprises Encountered Analysis Interpretation & Conclusion Karen Foster Julianne Ehlers Christopher Gleason Karen Foster Christopher Gleason John Farr Ron Grover

Purpose of the Study Is the number of shots on goal related to the number of goals scored in a soccer game?

Study Design This is an observational study of a simple random sample. The data collected will be the number of attempts to make a goal during a soccer game and the number of goals achieved. Each data set are discrete, quantitative values. Data collection will be completed by various members of the group. A minimum of 10 games will be observed. Randomness is achieved by creating no restrictions on location of the soccer game, skill level, age of players, time of day, weather or type of playing field. Examples of locations are Liberty Park, Dimple Dell Park and other local soccer fields.

Data, Statistics, & Graphs

Data Goals Attempted Goals Scored 16 4 4 2 8 3 5 4 11 8 7 3 9 5 10 3 12 5 11 4 9 3

Goals Attempted Statistics Mean: 9. 2727 Standard Deviation: 3. 3494 Five Number Summary: 4, 7. 5, 9, 11, 16 Range: 12 Mode: 9, 11 Outliers: None

Goals Attempted Graphs Histogram Frequency 2 Boxplot Goals Attempted 1 0 1 2 3 4 5 6 7 8 9 10 11 Goals Attempted 12 13 14 15 16

Goals Scored Statistics Mean: 4 Standard Deviation: 1. 6125 Five Number Summary: 2, 3, 4, 4. 5, 8 Range: 6 Mode: 3 Outliers: 8

Goals Scored Graphs Histogram 4 Boxplot Goals Scored Frequency 3 2 1 0 1 2 3 4 5 Goals Scored 6 7 8

Correlation Statistics & Scatterplot Linear Correlation Coefficient: 0. 4259 Equation for Line of Regression: ŷ = 0. 8846 x – 4. 2023

Difficulties & Surprises Encountered While gathering data we encountered several problems: It was difficult to find soccer games at the time the class had started, as it was winter and the outdoor soccer season hadn't even begun. To solve this, some group members opted to watch indoor soccer or watch games that had started early. Communication was difficult because all group members have different schedules. We decided to use email as our primary form of communication. One surprise encountered was keeping track of scores. If you didn't pay attention closely you could easily miss an attempt at the goal.

Analysis By viewing the histogram of the number of goals scored, the shape of the distribution for this variable is skewed to the right. By viewing the histogram of the shots on goal, the shape of the distribution is most closely associated with a bell-shaped distribution. According to the table found on the Neag Center for Gifted Education and Talent Development website (www. gifted. uconn. edu) there is not a statistically significant relationship between shots on goal and goals scored in our sample population. The lack of a statistically significant relationship is calculated by determining the degrees of freedom (2 minus sample size) and selecting the level of significance (0. 05). By using a df of 9 and a level of significance of 0. 05, the table lists 0. 602 as the minimum correlation coefficient possible or critical value to support a confidence interval of 95%. The correlation coefficient found from analyzing the data from the study is only 0. 4259 and therefore does not allow us to fail to reject the null hypothesis that there is no relationship.

Interpretation Based on intuitive reasoning, we would have answered the original question by stating that the number of shots on goal directly affects the number of goals scored in a game. The data tells a different story. We would now, based on the analysis of the data, say that there are more factors that determine the number of goals scored in a game. There are several lurking variables including the age of the players, skill level, and experience. There may be a goalie with many years experience that statistically would be able to keep more shots from going into the goal or a talented player that is very good at scoring goals. In the data collected there is no discernible correlation between the two variables. We see that even in games that have a low shots on goal number that the number of goals can be higher than average and vice-versa.

Conclusion Going back to the purpose of our study: Is the number of shots on goal related to the number of goals scored in a soccer game? The answer is NO! This study indicates that there can not be a direct correlation between the number of shots on goal during a game and the number of goals scored in that game.