· Answer all the questions. All questions are to be done using SPSS (or by hand, as stated).
· The questions are not of equal weight, and some questions are worth much more than others.
· When you are asked to comment on a finding, usually a short paragraph is all that is required.
· For all graphs, label the axes correctly, include a contextual title and the units of measurement. Titles and axes should be included by editing the SPSS graphic, and not by hand-writing the titles on the plot.
· In many cases, SPSS output contains much more information than is required for a correct and complete answer. Make sure you report only the information from the SPSS output relevant to your answer. Simply reproducing all SPSS output will result in a poor grade.
· Unless instructed otherwise, show all work and formulae used in calculating confidence intervals and performing hypothesis tests. (Answers may of course be checked where possible using software).
Use the information in the dataset auto.sav to answer ALL of the following questions.
Part I: SPSS file manipulation (10 points)
1. (3 points) The variable length contains the length of the car in inches. Create a new variable called “lenft” that has the length in feet instead of inches (12 inches = 1 foot).
2. (3 points) Suppose that we wanted to break mpg down into three categories. Create a new variable that is 1 for mpg <= 19, 2 for mpg between 19 and 23, and 3 for mpg >= 23. Call the variable “mpgcat”.
3. (4 points) Create a variable called mpgfd that assesses the mileage of the cars with respect to their origin. This variable, mpgfd, will have two values:
· 0 if below the median mpg for its group (foreign/domestic)
· 1 if at/above the median mpg for its group (foreign/domestic).
Take a screen shot of the VARIABLE VIEW of the SPSS spreadsheet when you are done. Upload the screen shot to Canvas. Title your screenshot “DA4_Part1_YourName.jpg” (where “YourName” is your name. The file could be .png, too). Points will be deducted for (1) Uploading the data view and (2) uploading both the data view and the variable view. In other words, part of your grade for this question is knowing the difference between variable view and data view.
Part II: Hypothesis Tests and Confidence Intervals in SPSS (40 points)
4. (3 points) Use SPSS to calculate the mean and standard deviation of weight of domestic cars (foreign = 0) from this sample. Select only those cars which are domestic for this question. Include the steps you used to answer this question.
5. (5 points) –Use the results in the previous question to estimate the mean weight for domestic cars in general, using a 98% confidence interval (show all work). Calculate the interval by hand. You may turn in your results on paper or via a photo uploaded to Canvas. If you upload a photo, make sure that it is only ONE file.
6. (2 points - Back to SPSS) Justify the use of the confidence interval formula by checking the appropriate conditions and assumptions (include appropriate statistics or ONE graph to support your answer).
7. (7 points) - Perform a hypothesis test to see if the true mean weight for domestic is less 3000 pounds. Calculate the test by hand and turn it in on paper. You may also upload a photo to Canvas as long as it is only ONE file). In performing this test, include:
a. The appropriate hypotheses (define any symbols used).
b. A statement of the assumptions for carrying out this test. Describe the assumptions in the context of this question, but do not check them.
c. Calculate a suitable test statistic for this test.
d. Calculate the P-value of this test.
e. Write a meaningful conclusion at the 5% level of significance.
8. (2 points) Check your answers for the previous problem by finding the value of the test statistic and the p-value using SPSS. [Copy and paste necessary SPSS output into this document. Include the steps to obtaining the output in your answer.]
9. (3 points) A researcher is interested in the performance of American and Japanese (foreign = 1) cars, in particular, do Japanese cars have a better fuel consumption (mpg) than American cars? Using SPSS and the sample information in auto.sav, determine the mean and standard deviation of fuel consumption for American and Japanese cars.
10. (3 points) Use an appropriate graph to compare the distribution of fuel consumption for Japanese and American cars.
11. (7 points) To answer the question `do Japanese cars have a better fuel consumption than American cars?’ perform a hypothesis test by completing the following:
a. State appropriate hypothesis, clearly defining all symbols.
b. Check the assumptions for carrying out this test.
c. Without using SPSS, calculate a suitable test statistic (you can use the descriptive statistics calculated from SPSS in this calculation).
d. Without using SPSS, find the P-value of the test.
e. Interpret the P-value and describe the outcome of the original question.
12. (2 points) Now use SPSS to check your results for this hypothesis test. Copy and paste the relevant output from SPSS for this test to your assignment.
13. (3 points) Briefly comment on how the test statistic and P-value from SPSS output are similar to or different from your hand calculations.
14. (3 points) In 100 words or less, describe any issues you can see in conducting this test. Include tables or diagrams if needed.