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A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below. Vacation Days 6 3 10 0 15 8 11 0 4 0 0 6 1 Sick Days 1 0 4 0 9 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: p ✓ = 0 H₁: p✓✓ #0 O The p-value is: (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. There is statistically significant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the regression line is useful. O There is statistically significant evidence to conclude that an employee who takes more vacation days will take more sick days than an employee who takes fewer vacation days. O There is statistically insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the use of the regression line is not appropriate. O There is statistically significant evidence to conclude that an employee who takes more vacation days will take fewer sick days than an employee who takes fewer vacation days d. 7² (Round to two decimal places)

A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below. Vacation Days 6 3 10 0 15 8 11 0 4 0 0 6 1 Sick Days 1 0 4 0 9 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: p ✓ = 0 H₁: p✓✓ #0 O The p-value is: (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. There is statistically significant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the regression line is useful. O There is statistically significant evidence to conclude that an employee who takes more vacation days will take more sick days than an employee who takes fewer vacation days. O There is statistically insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the use of the regression line is not appropriate. O There is statistically significant evidence to conclude that an employee who takes more vacation days will take fewer sick days than an employee who takes fewer vacation days d. 7² (Round to two decimal places)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Relationship Between Vacation Days and Sick Days **Study Overview:** A study was conducted to examine the relationship between the number of vacation days employees take each year and the number of sick days they take annually. The survey results are provided below: | | **Vacation Days** | 6 | 15 | 8 | 11 | 0 | 4 | 3 | 10 | 0 | | -------- | ----------------- | - | -- | - | -- | - | - | - | -- | - | | **Sick Days** | 1 | 0 | 0 | 0 | 6 | 4 | 0 | 9 | ### Analysis: **a. Find the Correlation Coefficient:** The correlation coefficient (\(r\)) needs to be calculated and rounded to 2 decimal places. **b. Null and Alternative Hypotheses for Correlation:** - **Null Hypothesis (H₀):** \(\rho = 0\) - **Alternative Hypothesis (H₁):** \(\rho \neq 0\) **c. P-value Calculation:** The p-value needs to be calculated and rounded to four decimal places. **d. Conclusion of Hypothesis Test:** Using a significance level of \(\alpha = 0.05\), choose one of the following conclusions based on the hypothesis test in the context of the study: - **Option 1:** There is statistically significant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the regression line is useful. - **Option 2:** There is statistically significant evidence to conclude that an employee who takes more vacation days will take more sick days than an employee who takes fewer vacation days. - **Option 3:** There is statistically insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the use of the regression line is not appropriate. - **Option 4:** There is statistically significant evidence to conclude that an employee who takes more vacation days will take fewer sick days than an employee who takes fewer vacation days. **e. Calculate \( r^2 \):** - Round \( r^2 \) to two decimal places. ### Understanding Graphs and Diagrams: No graph or diagram is provided directly in the study here. However, typically, a scatter plot would be
Transcribed Image Text:### Relationship Between Vacation Days and Sick Days **Study Overview:** A study was conducted to examine the relationship between the number of vacation days employees take each year and the number of sick days they take annually. The survey results are provided below: | | **Vacation Days** | 6 | 15 | 8 | 11 | 0 | 4 | 3 | 10 | 0 | | -------- | ----------------- | - | -- | - | -- | - | - | - | -- | - | | **Sick Days** | 1 | 0 | 0 | 0 | 6 | 4 | 0 | 9 | ### Analysis: **a. Find the Correlation Coefficient:** The correlation coefficient (\(r\)) needs to be calculated and rounded to 2 decimal places. **b. Null and Alternative Hypotheses for Correlation:** - **Null Hypothesis (H₀):** \(\rho = 0\) - **Alternative Hypothesis (H₁):** \(\rho \neq 0\) **c. P-value Calculation:** The p-value needs to be calculated and rounded to four decimal places. **d. Conclusion of Hypothesis Test:** Using a significance level of \(\alpha = 0.05\), choose one of the following conclusions based on the hypothesis test in the context of the study: - **Option 1:** There is statistically significant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the regression line is useful. - **Option 2:** There is statistically significant evidence to conclude that an employee who takes more vacation days will take more sick days than an employee who takes fewer vacation days. - **Option 3:** There is statistically insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the use of the regression line is not appropriate. - **Option 4:** There is statistically significant evidence to conclude that an employee who takes more vacation days will take fewer sick days than an employee who takes fewer vacation days. **e. Calculate \( r^2 \):** - Round \( r^2 \) to two decimal places. ### Understanding Graphs and Diagrams: No graph or diagram is provided directly in the study here. However, typically, a scatter plot would be
### Linear Regression Analysis on Vacation and Sick Days #### f. Equation of the Linear Regression Line The equation of the linear regression line is: \[ \hat{y} = \text{\_\_\_\_} + \text{\_\_\_\_}x \] (Please show your answers to two decimal places). #### g. Predicting Sick Days Use the model to predict the number of sick days taken for an employee who took 3 vacation days this year. \[ \text{Sick Days} = \text{\_\_\_\_} \] (Please round your answer to the nearest whole number). #### h. Interpretation of the Slope Interpret the slope of the regression line in the context of the question: - The slope has no practical meaning since a negative number cannot occur with vacation days and sick days. - As x goes up, y goes down. - \(\checkmark\) For every additional vacation day taken, employees tend to take on average 0.53 fewer sick days. #### i. Interpretation of the y-intercept Interpret the y-intercept in the context of the question: - If an employee takes no vacation days, then that employee will take 6 sick days. - \(\checkmark\) The best prediction for an employee who doesn’t take any vacation days is that the employee will take 6 sick days. - The y-intercept has no practical meaning for this study. This content is designed to help you understand linear regression and how it can be used to analyze and interpret the relationship between two variables—in this case, vacation days and sick days taken by employees.
Transcribed Image Text:### Linear Regression Analysis on Vacation and Sick Days #### f. Equation of the Linear Regression Line The equation of the linear regression line is: \[ \hat{y} = \text{\_\_\_\_} + \text{\_\_\_\_}x \] (Please show your answers to two decimal places). #### g. Predicting Sick Days Use the model to predict the number of sick days taken for an employee who took 3 vacation days this year. \[ \text{Sick Days} = \text{\_\_\_\_} \] (Please round your answer to the nearest whole number). #### h. Interpretation of the Slope Interpret the slope of the regression line in the context of the question: - The slope has no practical meaning since a negative number cannot occur with vacation days and sick days. - As x goes up, y goes down. - \(\checkmark\) For every additional vacation day taken, employees tend to take on average 0.53 fewer sick days. #### i. Interpretation of the y-intercept Interpret the y-intercept in the context of the question: - If an employee takes no vacation days, then that employee will take 6 sick days. - \(\checkmark\) The best prediction for an employee who doesn’t take any vacation days is that the employee will take 6 sick days. - The y-intercept has no practical meaning for this study. This content is designed to help you understand linear regression and how it can be used to analyze and interpret the relationship between two variables—in this case, vacation days and sick days taken by employees.
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