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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 1 Sick Days 6 15 8 8 14 13 0 0 2 0 0 10 0 11 0 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho: ? ☺ = 0 H₁: ? 0 The p-value is: Round to 3 decimal places. 15 3 0 9 Round to 4 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 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. 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. 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. 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. The equation of the linear regression line is: ŷ = (Please show your answers to 3 decimal places) e. Predict the number of sick days taken for an employee who took 5 vacation days this year. Remember to only use the model if you found that there is linear relationship between the variables. Otherwise, you should use the average of the y-values. Sick Days = (Please round your answer to the nearest whole number.)

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 1 Sick Days 6 15 8 8 14 13 0 0 2 0 0 10 0 11 0 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho: ? ☺ = 0 H₁: ? 0 The p-value is: Round to 3 decimal places. 15 3 0 9 Round to 4 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 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. 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. 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. 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. The equation of the linear regression line is: ŷ = (Please show your answers to 3 decimal places) e. Predict the number of sick days taken for an employee who took 5 vacation days this year. Remember to only use the model if you found that there is linear relationship between the variables. Otherwise, you should use the average of the y-values. Sick Days = (Please round your answer to the nearest whole number.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
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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 1 Sick Days 6 15 0 8 0 8 14 13 2 0 = c. Use a level of significance of a the study. 10 0 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H₁: ? Ⓒ 0 The p-value is: 11 + = 0 Round to 4 decimal places. 15 3 0 9 Round to 3 decimal places. 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. 0.05 to state the conclusion of the hypothesis test in the context of 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. 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. 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. The equation of the linear regression line is: y = X (Please show your answers to 3 decimal places) e. Predict the number of sick days taken for an employee who took 5 vacation days this year. Remember to only use the model if you found that there is linear relationship between the variables. Otherwise, you should use the average of the y-values. Sick Days (Please round your answer to the nearest whole number.)
Transcribed Image Text: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 1 Sick Days 6 15 0 8 0 8 14 13 2 0 = c. Use a level of significance of a the study. 10 0 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H₁: ? Ⓒ 0 The p-value is: 11 + = 0 Round to 4 decimal places. 15 3 0 9 Round to 3 decimal places. 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. 0.05 to state the conclusion of the hypothesis test in the context of 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. 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. 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. The equation of the linear regression line is: y = X (Please show your answers to 3 decimal places) e. Predict the number of sick days taken for an employee who took 5 vacation days this year. Remember to only use the model if you found that there is linear relationship between the variables. Otherwise, you should use the average of the y-values. Sick Days (Please round your answer to the nearest whole number.)
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