Know the definitions of the following:
Individual
Variable
Categorical variable
Quantitative variable
Distribution
Histogram
Unimodal distribution
Symmetric distribution
Outlier
Mean
Median
Quartile
Interquartile range
Standard deviation
Normal distribution
Explanatory variable
Response variable
Correlation
Regression line
Residual
Lurking variable
Common response
Confounding
Anecdotal evidence
Experiment
Observational study
Factor
Subject
Treatment
Block design
Stratification
Bias
Parameter
Statistic
The following sample questions cover the more mathematical sorts of questions I may ask.
1. The mean and median salaries paid to major league baseball players in 1993 were $490,000 and $1,160,000. Which of these numbers is the mean, and which is the median?
2. The psychology department at a major university is doing a study of the GRE scores of its applicants for graduate study. The applicants have a mean GRE score of 544 with a standard deviation of 103. If the department places a cut-off for admission of 650, what portion of the department's applicants will be rejected by this rule?
3. The department is also considering using GRE scores as part of the criteria for deciding which graduate students get offered research assistanceships. The department wants to use the GRE score to generate an initial pool of the top 20% of applicants that would then be narrowed down by more careful selection methods. Where would the department have to place the cutoff to catch the top 20% of the applicant pool?
4. Joan is concerned about the amount of energy she uses to heat her home in the Midwest. She keeps a record of the natural gas she consumes each month over one year's heating season. Because the months are not all the same length, she divides each month's consumption by the number of days in the month to get the average number of cubic feet of gas used per day. Demand for heating is strongly influenced by the outside temperature. From local weather records, Joan obtains the average number of heating degree-days per day for each month. Here are Joan's data
| Month | Degree-days | Gas consumed |
|---|---|---|
| Oct. | 15.6 | 520 |
| Nov. | 26.8 | 610 |
| Dec. | 37.8 | 870 |
| Jan. | 36.4 | 850 |
| Feb. | 35.5 | 880 |
| Mar. | 18.6 | 490 |
| Apr. | 15.3 | 450 |
| May | 7.9 | 250 |
| June | 0.0 | 110 |
Plot this data, compute the regression line, and plot it.
5. Joan adds insulation in her attic during the summer, hoping to reduce her gas consumption. The next February, there are an average of 40 degree-days per day and her gas consumption is 870 cubic feet per day. Predict from the regression equation how much gas the house would have used at 40 degree-days per day last winter before the extra insulation.
6. A business has 2000 male and 500 female employees. The equal opportunity employment officer wants to poll the opinions of a random sample of employees. In order to give adequate attention to female employee opinion, he decides to choose a stratified random sample of 200 males and 200 females. He has alphabetized lists of female and male employees. Explain how you would assign labels and use random digits to choose the desired sample. Enter Table B at line 122 and give the labels of the first 5 females and the first 5 males in the sample.