In: Statistics and Probability
Professor Smith wants to determine if a correlation exists between absences and final grade. She determines the number of absences for ten students in her class and then determines the mean final score for those students. Below are her data:
Student Absences Score
1................. 0...........95
2................. 1.......... 90
3................. 4.......... 72
4................. 3.......... 78
5................. 2.......... 84
6................. 5.......... 67
7................. 4.......... 71
8................. 2.......... 80
9................. 7.......... 55
10............... 5 ......... 64
1. State the null hypothesis: ______________________
2. The Independent Variable is: ________________________
3. The Dependent Variable is: ________________________
4. Pearson's R = _______________ Positive or Negative? ____________________
5. The R is: Strong ___________ Moderate ____________ Weak _____________
6. The Coefficient of Determination is: _________________________
7. The t statistic is ______________ Significant at the __________ level.
8. What percent pf the change in the dependent variable can be attributed to the independent variable? _______%
9. If a student has 6 absences, what would their final scores likely be? ________________
10. State your conclusion. Do you reject the null hypothesis? Is attendance important in order to get a good grade in Professor Smith's class?
1)
Explanation: The null hypothesis is defined as there is no correlation between absences and the final grade of a student.
2)
Independent Variable: number of absences
Explanation: Since we want to see the effect of the number of absences on the final grade score of a student, the variable number of absences is free to vary thus the number of absences is an Independent Variable
3)
Dependent Variable: Final grade score.
Explanation: Since the final grade score dependent on the number of absences, it is a dependent variable.
4)
Pearson's R = -0.9933. Negative.
Explanation: Pearson's correlation coefficient value is obtained in excel using the function =CORREL(). The screenshot is shown below,
5)
The R is: Strong
Explanation: Since the Pearson's correlation coefficient value is close 1, there is a strong correlation between absences and the final grade of a student (R = 0.8 to 1 considers as strong).
6)
The Coefficient of Determination is: 0.9866
Explanation: The Coefficient of Determination (R square) value is obtained by taking the square of the Pearson's correlation coefficient value as shown below,
7)
The t statistic is -24.2947 Significant at the 1% significance level.
Explanation:
The t-statistic is obtained using the formula,
The p-value is obtained from the t distribution table for the degree of freedom = n-2=8
8)
The change in the dependent variable can be attributed to the independent variable 98.66%
Explanation: The R square value gives the proportion of the dependent variable that is explained by the independent variable.
9)
final score = 60.0599
Explanation:
The regression equation is defined as,
The least-square estimate of intercept and slope is obtained in excel. The screenshot is shown below,
The regression equation is,
For Absences = 6,
10)
Reject the null hypothesis. Attendance is important in order to get a good grade in Professor Smith's class.
Explanation: From the correlation hypothesis test, the p-value < 0.01 hence the null hypothesis is rejected at a 1% significance level which means there is a significant correlation between absences and the final grade of a student.