Midterm and Final Exam Scores for 58 Business Statistics Students Midterm Exam Score Final Exam Score 80 78 87 85 72 81 69 54 86 70 83 73 78 89 75 84 74 86 75 79 84 75 73 63 74 72 73 69 80 86 75 78 72 75 77 68 76 77 66 78 74 77 71 73 85 79 74 74 76 79 76 73 84 72 77 81 78 86 86 76 81 83 78 83 85 86 73 71 83 83 83 79 72 68 83 90 84 89 73 83 86 81 76 79 58 58 73 77 81 85 72 67 77 70 82 79 64 59 79 74 79 86 82 85 75 79 78 81 58 31 80 82 68 70 73 69 4446 4417 Choose the dependent variable (the response variable to be "explained") and the independent variable (the predictor or explanatory variable). (a-1) Dependent Variable Midterm Exam Score Final Exam Score (a-2) Independent Variable Midterm Exam Score Final Exam Score (b) Obtain the regression equation. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.) Y = X + (c) Calculate R2. (Round your answer to 4 decimal places.) R2 (d-1) Zero is contained in the 95% confidence interval. Yes No (d-2) The slope is different from zero. Yes No (e) Calculate the degrees of freedom and t-critical for a two-tailed t test for zero slope at α = .05. (Round your answers to 2 decimal places.) Degrees of freedom t - critical ± (f-1) Small p-values tell us the null hypothesis is false. Yes No (f-2) The sample provides significant evidence that the slope is negative. Yes No
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
| Midterm and Final Exam Scores for 58 Business Statistics Students | |||||||
| Midterm Exam Score | Final Exam Score |
|
|||||
| 80 | 78 | ||||||
| 87 | 85 | ||||||
| 72 | 81 | ||||||
| 69 | 54 | ||||||
| 86 | 70 | ||||||
| 83 | 73 | ||||||
| 78 | 89 | ||||||
| 75 | 84 | ||||||
| 74 | 86 | ||||||
| 75 | 79 |
|
|||||
| 84 | 75 | ||||||
| 73 | 63 | ||||||
| 74 | 72 | ||||||
| 73 | 69 | ||||||
| 80 | 86 | ||||||
| 75 | 78 | ||||||
| 72 | 75 | ||||||
| 77 | 68 | ||||||
| 76 | 77 | ||||||
| 66 | 78 | ||||||
| 74 | 77 | ||||||
| 71 | 73 | ||||||
| 85 | 79 | ||||||
| 74 | 74 | ||||||
| 76 | 79 | ||||||
| 76 | 73 | ||||||
| 84 | 72 | ||||||
| 77 | 81 | ||||||
| 78 | 86 | ||||||
| 86 | 76 | ||||||
| 81 | 83 | ||||||
| 78 | 83 | ||||||
| 85 | 86 | ||||||
| 73 | 71 | ||||||
| 83 | 83 | ||||||
| 83 | 79 | ||||||
| 72 | 68 | ||||||
| 83 | 90 | ||||||
| 84 | 89 | ||||||
| 73 | 83 | ||||||
| 86 | 81 | ||||||
| 76 | 79 | ||||||
| 58 | 58 | ||||||
| 73 | 77 | ||||||
| 81 | 85 | ||||||
| 72 | 67 | ||||||
| 77 | 70 | ||||||
| 82 | 79 | ||||||
| 64 | 59 | ||||||
| 79 | 74 | ||||||
| 79 | 86 | ||||||
| 82 | 85 | ||||||
| 75 | 79 | ||||||
| 78 | 81 | ||||||
| 58 | 31 | ||||||
| 80 | 82 | ||||||
| 68 | 70 | ||||||
| 73 | 69 | ||||||
| 4446 | 4417 |
Choose the dependent variable (the response variable to be "explained") and the independent variable (the predictor or explanatory variable).
(a-1) Dependent Variable
-
Midterm Exam Score
-
Final Exam Score
(a-2) Independent Variable
-
Midterm Exam Score
-
Final Exam Score
(b) Obtain the regression equation. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
Y = X +
(c) Calculate R2. (Round your answer to 4 decimal places.)
R2
(d-1) Zero is contained in the 95% confidence interval.
-
Yes
-
No
(d-2) The slope is different from zero.
-
Yes
-
No
(e) Calculate the degrees of freedom and t-critical for a two-tailed t test for zero slope at α = .05. (Round your answers to 2 decimal places.)
| Degrees of freedom | |
| t - critical | ± |
(f-1) Small p-values tell us the null hypothesis is false.
-
Yes
-
No
(f-2) The sample provides significant evidence that the slope is negative.
-
Yes
-
No
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