Homework 3
Use the specific data provided for each problem.
1. Stocks Data: An investor portfolio seems to be underperforming. She was promised a portfolio that would ‘mirror’ the returns of the entire U.S. stock market. A sample of 39 monthly returns of her portfolio is provided (variable 1, stocks). Test to see if the portfolio did in fact provide the returns of the U.S. Stock market. Over the same 39 months, the S&P 500 had a monthly average return of .95%.
a. What are the sample mean and standard deviation for the portfolio?
b. What are the correct null and alternative hypotheses? Assume that a neutral
arbitration panel is conducting the test.
c. What are the results of the test?
d. How much different than the S&P was the portfolio? Use 95% confidence.
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e. Should damages be awarded to the owner of the portfolio? If so, how would you approximate a fair amount?
2. Machine Capacity (variable 4): An engineering team is tasked with improving the maximum capacity of a recycling plant. The current average capacity is 33,000 pounds per hour. A sample of 90 hours was taken to test whether the changes were successful.
a. Are there any outliers in the data?
b. Using all 90 hours of data, test to see if the process was improved. State your results.
c. Estimate the machine capacity after the improvements. Use 95% confidence.
d. There are three compensation levels for the engineers: 1. Time only- if the changes were not successful, 2. Time plus standard fee- if the changes were successful at 5% level of significance, 3. Time, fee plus bonus- if improvements were highly significant (1% alpha). Which should the team be paid and why?
3. French language instruction: Using variables 2 and 3, consider the effectiveness of a French language instructional program. Your company uses the program to prepare executives for business in France. Each of the executives participating were given a pre test and, after the program, a post test.
a. What method is most useful to test the effectiveness of the program?
b. What are the test results?
c. What is your estimate of the average score change? Use 95% confidence.
d. If you were arguing in favor of keeping the program, what evidence could you sight from your test/estimate? If you wanted to cut the program funding, what evidence could you site?
4. Computer vs. Driver (variables 5 and 6): Many automobiles have computers that track average fuel economy. Fuel economy is major selling point. A consumer protection group is concerned that autos might overestimate the actual mileage and so an experiment to test the computer’s estimate is designed.
a. Test to see if the difference between the computer and the driver mileage numbers is highly significant. What are your results?
b. What is the average difference between the computer and the driver?
c. What is your estimate of the true average difference? Use 95% confidence.
d. Do you see any problem with the computer estimate of mileage? Is the difference, if any, explainable?
5. Image Priming: Image priming is used in advertising. If a consumer is ‘primed’ to see an image, they have a prior impression of what the image means, independently of the product being advertised with the image. (Think of a wine label with a picture of zebra- zebras have nothing to do with wine but an image of a zebra may be associated with a particular feeling. Or think of ad for lemonade that has a picture of front-porch swing). The effectiveness of an ad, in theory, should be improved if the target market is ‘primed’ to perceive images in a particular way.
A sample of 42 respondents answered Yes or No when asked if the image being used in an ad meant anything to them. Then they viewed an ad using that image. Then scored the effectiveness of the ad 1-5, 5 being best.
Test to see if the Yes group has a significantly higher average score than the No group. What are your results? What is your estimate of mean score difference? Use 95% confidence. Does image priming seem to work based on this experiment?
6. Gender and Survey of Study Habits and Attitudes (SSHA): Using the sample provided, consider the relationship between gender and SSHA score.
a. Check each sample carefully for any outliers/skew.
b. Test to see if there is a significant difference in average SSHA between genders. What are your results?
c. What do these results allow you to conclude?
d. What is the limitation of this study? In other words, what is the potential risk in generalizing your conclusion to the entire population of college students?