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A researcher is interested in seeing if there is a correlation between number of hours a person drives and the amount of fuel (in gallons) that is left in the gas tank. He starts with a pilot test using data for four people…
|
Number of Hours Driving (x) |
Gallons of Fuel Left in Tank (y) |
|
|
3 |
4 |
|
|
2 |
5 |
|
|
1 |
9 |
|
|
6 |
1. What is the correlation coefficient for the above data? What does it tell us about the relationship between hours of driving and the number of gallons of gasoline left in the gas tank?
(NOTE: there is specific information on how to calculate correlation coefficients using StatCrunch in Module 2 on page 4 of 8 of the Linear Relationship in the Learn By Doing: Linear Relationships activity at the bottom of the page. Instead of loading a file, however, do the following:
Click on: Open StatCrunch
Enter data into the spreadsheet, exactly as it appears in the above table, using the first row for the variable names and putting the numbers in row 1-4 [since there are 4 pairs of data])
2. What is the least-squares regression line for the above data? (NOTE: there is specific information on how to use the correlation coefficient. means, and standard deviations from the samples to determine the slope, intercept, and regression line using the formula on the top of page 54 Linear Relationships (7 of 8).
3. Using the least-squares regression line from question 2, find out what the predicted level of gasoline would be for a person who drives 5 hours.
4. Based on the results from this pilot study, the researcher decides to conduct a larger study to see if the results hold up with a larger sample. The selection of a sampling technique is a very important consideration for researchers, since it affects the ability to take a study’s results and generalize it to other groups of people (a main concern for researchers) (Note: You will learn more about the ability to generalize from a sample to a population in the research methods course.). Based on what you have learned from Module 3 on sampling, what sampling technique would you recommend that the researcher use and why? What are its possible strengths and limitations. Be sure to provide a description of the technique and how it would be implemented. (Note: There are many possible choices that would work for the study. I am interested in seeing that you understand and apply the technique correctly as well as understand its benefits and limitations.).
