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What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 12 randomly selected games are shown below. Attendance Runs 25 34 42 2 9 8 0 23 29 30 45 3 3 3 11 0 20 42 7 7 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: H₂:2 H₁: ? The p-value is: 51 22 29 9 3 8 Round to 2 decimal places. (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful. O There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance. O There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance.

What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 12 randomly selected games are shown below. Attendance Runs 25 34 42 2 9 8 0 23 29 30 45 3 3 3 11 0 20 42 7 7 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: H₂:2 H₁: ? The p-value is: 51 22 29 9 3 8 Round to 2 decimal places. (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful. O There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance. O There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.2: Box-and-whisker Plots
Problem 1E
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**Analysis of Relationship between Attendance at Major League Baseball Games and Total Runs Scored** This study examines the relationship between attendance figures (in thousands) and the total number of runs scored for 12 randomly selected major league baseball games. The data is presented as follows: | Attendance | 25 | 34 | 42 | 23 | 29 | 40 | 45 | 20 | 42 | 51 | 22 | 29 | |------------|----|----|----|----|----|----|----|----|----|----|----|----| | Runs | 2 | 9 | 8 | 3 | 3 | 11 | 7 | 7 | 9 | 3 | 8 | 8 | ### Statistical Analysis a. **Correlation Coefficient (r):** - Find the correlation coefficient and round to two decimal places. b. **Hypotheses for Correlation:** - Null Hypothesis (\(H_0\)): \(\rho = 0\) - Alternative Hypothesis (\(H_1\)): \(\rho \neq 0\) - Determine the p-value and round to four decimal places. c. **Significance Test (\(\alpha = 0.05\)):** - Evaluate the statistical significance of the correlation: 1. Strong evidence that correlation exists. Regression line useful. 2. Strong evidence negative correlation exists. High attendance leads to fewer runs. 3. Strong evidence positive correlation exists. High attendance leads to more runs. 4. Insignificant evidence for stating correlation. Regression line not appropriate. d. **Coefficient of Determination (r²):** - Compute r² value and round to two decimal places. e. **Interpretation of \(r²\):** - 49% of all games will have an average number of runs scored. - A given attendance results in 49% of games with the predicted runs. - Large variation in runs reduced by 49%. - 49% chance the regression line predicts runs accurately. f. **Equation of the Linear Regression Line:** - \( \hat{y} = b_0 + b_1x \) - Calculate and round values to two decimal places. g. **Prediction:** - Use the
Transcribed Image Text:**Analysis of Relationship between Attendance at Major League Baseball Games and Total Runs Scored** This study examines the relationship between attendance figures (in thousands) and the total number of runs scored for 12 randomly selected major league baseball games. The data is presented as follows: | Attendance | 25 | 34 | 42 | 23 | 29 | 40 | 45 | 20 | 42 | 51 | 22 | 29 | |------------|----|----|----|----|----|----|----|----|----|----|----|----| | Runs | 2 | 9 | 8 | 3 | 3 | 11 | 7 | 7 | 9 | 3 | 8 | 8 | ### Statistical Analysis a. **Correlation Coefficient (r):** - Find the correlation coefficient and round to two decimal places. b. **Hypotheses for Correlation:** - Null Hypothesis (\(H_0\)): \(\rho = 0\) - Alternative Hypothesis (\(H_1\)): \(\rho \neq 0\) - Determine the p-value and round to four decimal places. c. **Significance Test (\(\alpha = 0.05\)):** - Evaluate the statistical significance of the correlation: 1. Strong evidence that correlation exists. Regression line useful. 2. Strong evidence negative correlation exists. High attendance leads to fewer runs. 3. Strong evidence positive correlation exists. High attendance leads to more runs. 4. Insignificant evidence for stating correlation. Regression line not appropriate. d. **Coefficient of Determination (r²):** - Compute r² value and round to two decimal places. e. **Interpretation of \(r²\):** - 49% of all games will have an average number of runs scored. - A given attendance results in 49% of games with the predicted runs. - Large variation in runs reduced by 49%. - 49% chance the regression line predicts runs accurately. f. **Equation of the Linear Regression Line:** - \( \hat{y} = b_0 + b_1x \) - Calculate and round values to two decimal places. g. **Prediction:** - Use the
<h2>Understanding Regression Line Analysis</h2> <h3>h. Interpreting the Slope in Context:</h3> <ul> <li>For every additional thousand people who attend a game, there tends to be an average increase of 0.21 runs scored.</li> <li>The slope has no practical meaning since the total number of runs scored in a game must be positive.</li> <li>As x goes up, y goes up.</li> </ul> <h3>i. Interpreting the Y-Intercept in Context:</h3> <ul> <li>The best prediction for a game with 0 attendance is that there will be -1 runs scored.</li> <li>If the attendance of a baseball game is 0, then -1 runs will be scored.</li> <li>The average runs scored is predicted to be -1.</li> <li>The y-intercept has no practical meaning for this study.</li> </ul>
Transcribed Image Text:<h2>Understanding Regression Line Analysis</h2> <h3>h. Interpreting the Slope in Context:</h3> <ul> <li>For every additional thousand people who attend a game, there tends to be an average increase of 0.21 runs scored.</li> <li>The slope has no practical meaning since the total number of runs scored in a game must be positive.</li> <li>As x goes up, y goes up.</li> </ul> <h3>i. Interpreting the Y-Intercept in Context:</h3> <ul> <li>The best prediction for a game with 0 attendance is that there will be -1 runs scored.</li> <li>If the attendance of a baseball game is 0, then -1 runs will be scored.</li> <li>The average runs scored is predicted to be -1.</li> <li>The y-intercept has no practical meaning for this study.</li> </ul>
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