The following data give the number of hours 5 students spent studying and their corresponding grades on their midterm exams. Hours studying 3 3 4 5 5 Midterm grades 72 74 74 75 79 Summation Table X Y XY X2 Y2 Exam 1 3 72 216 9 5184 Exam 2 3 74 222 9 5476 Exam 3 4 74 296 16 5476 Exam 4 5 75 375 25 5625 Exam 5 5 79 395 25 6241 SUM 20 374 1504 84 28002 Step 1: Calculate the sum of squared errors. Use the values b0=66.8000 and b1= 2.0000 for the calculations. Step 2: Calculate the estimated variance of errors, s2e. Step 3: Calculate the estimated variance of slope s2b1.
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.
The following data give the number of hours 5 students spent studying and their corresponding grades on their midterm exams.
| Hours studying | 3 | 3 | 4 | 5 | 5 |
| Midterm grades | 72 | 74 | 74 | 75 | 79 |
Summation Table
| X | Y | XY | X2 | Y2 | |
| Exam 1 | 3 | 72 | 216 | 9 | 5184 |
| Exam 2 | 3 | 74 | 222 | 9 | 5476 |
| Exam 3 | 4 | 74 | 296 | 16 | 5476 |
| Exam 4 | 5 | 75 | 375 | 25 | 5625 |
| Exam 5 | 5 | 79 | 395 | 25 | 6241 |
| SUM | 20 | 374 | 1504 | 84 | 28002 |
Step 1: Calculate the sum of squared errors. Use the values b0=66.8000 and b1= 2.0000 for the calculations.
Step 2: Calculate the estimated variance of errors, s2e.
Step 3: Calculate the estimated variance of slope s2b1.
Step 4: Construct the 80% confidence interval for the slope.
lower endpoint:
upper endpoint:
Step 5: Construct the 98% confidence interval for the slope.
Lower endpoint
Upper endpoint
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