Now look at the variable DIFFERENCE in the data file “Fuel Efficiency.” If there is no difference between the computer-calculated and driver-calculated mpg, then the average DIFFERENCE should be zero. Calculate the 95% confidence Interval for variable DIFFERENCE. Do your calculation step-by-step and fill out the values in the diagrams below. First use Excel Descriptive Statistics to get the two important statistics: sample-mean estimate ?̅ and the standard deviation s. Fill-Up No. Computer Driver Difference 1 41.5 36.5 5 2 50.7 44.2 6.5 3 36.6 37.2 -0.6 4 37.3 35.6 1.7 5 34.2 30.5 3.7 6 45 40.5 4.5 7 48 40 8 8 43.2 41 2.2 9 47.7 42.8 4.9 10 42.2 39.2 3 11 43.2 38.8 4.4 12 44.6 44.5 0.1 13 48.4 45.4 3 14 46.4 45.3 1.1 15 46.8 45.7 1.1 16 39.2 34.2 5 17 37.3 35.2 2.1 18 43.5 39.8 3.7 19 44.3 44.9 -0.6 20 43.3 47.5 -4.2 • What is the sample mean estimate ?̅ ? ?̅= ___________________ • What is the standard deviation s of the sample? s = ___________________ What is Standard Error of the Sample Mean: sX̅ =_____________________ What is the critical value: t* = ______ (Use the t-Table, df = n - 1 = 20-1 = 19) The margin of error: m = t*× ??̅ = _____________________________________ Lower Confidence Level = ?̅- m = ___________________________________________ Upper Confidence Level = ?̅+ m = ____________________________________________
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Now look at the variable DIFFERENCE in the data file “Fuel Efficiency.” If there is no difference between the computer-calculated and driver-calculated mpg, then the average DIFFERENCE should be zero. Calculate the 95% confidence Interval for variable DIFFERENCE. Do your calculation step-by-step and fill out the values in the diagrams below. First use Excel
| Fill-Up No. | Computer | Driver | Difference |
| 1 | 41.5 | 36.5 | 5 |
| 2 | 50.7 | 44.2 | 6.5 |
| 3 | 36.6 | 37.2 | -0.6 |
| 4 | 37.3 | 35.6 | 1.7 |
| 5 | 34.2 | 30.5 | 3.7 |
| 6 | 45 | 40.5 | 4.5 |
| 7 | 48 | 40 | 8 |
| 8 | 43.2 | 41 | 2.2 |
| 9 | 47.7 | 42.8 | 4.9 |
| 10 | 42.2 | 39.2 | 3 |
| 11 | 43.2 | 38.8 | 4.4 |
| 12 | 44.6 | 44.5 | 0.1 |
| 13 | 48.4 | 45.4 | 3 |
| 14 | 46.4 | 45.3 | 1.1 |
| 15 | 46.8 | 45.7 | 1.1 |
| 16 | 39.2 | 34.2 | 5 |
| 17 | 37.3 | 35.2 | 2.1 |
| 18 | 43.5 | 39.8 | 3.7 |
| 19 | 44.3 | 44.9 | -0.6 |
| 20 | 43.3 | 47.5 | -4.2 |
• What is the sample mean estimate ?̅ ? ?̅= ___________________
• What is the standard deviation s of the sample? s = ___________________
What is Standard Error of the Sample Mean: sX̅ =_____________________
What is the critical value: t* = ______ (Use the t-Table, df = n - 1 = 20-1 = 19)
The margin of error: m = t*× ??̅ = _____________________________________
Lower Confidence Level = ?̅- m = ___________________________________________ Upper Confidence Level = ?̅+ m = ____________________________________________
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