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| 科目： 統 計 學 |
|
I.
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Multiple Choice Questions: (45 points, 3 points for each. There is only ONE correct answer for each of the following question.) |
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1.
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A nonparametric method that is equivalent to the Wilcoxon rank sum test is the |
| (a) Mann-Whitney test. | |
| (b) Friedman test. | |
| (c) Kruskal-Wallis test. | |
| (d) Wilcoxon signed rank sum test. | |
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2.
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For which one of the following types of scales the mode is the most appropriate measure of central tendency? |
| (a) Ordinal | |
| (b) Ratio | |
| (c) Nominal | |
| (d) Interval. | |
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3.
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Which of the following is not one of the rules we should use to choose the proper significance test? |
| (a) Is the measurement scale nominal, ratio, interval or ordinal? | |
| (b) Are the samples related or independent? | |
| (c) Does the test involve one sample, two samples, or k samples? | |
| (d) Is the case one-tailed or two-tailed? | |
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4.
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Which of the following statements about the Chi-Square test is INCORRECT? |
| (a) It is widely used as anonparametric test for normally scaled data. | |
| (b) It is used only when the population is viewed as of only two classes. | |
| (c) It tests for significant differences between the observed and expected distributions. | |
| (d) Can also be used with kindependent sample. | |
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5.
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The standard error of the mean is |
| (a) the standard deviation of the distribution of sample means | |
| (b) the average difference between the sample means | |
| (c) the average difference between the population mean | |
| (d) the average of the sample means. | |
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6.
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Bayesian statistics use |
| (a) only sample data. | |
| (b) only subjective probabilities. | |
| (c) posterior distributions which are invariant. | |
| (d) sample data and subjective probabilities. | |
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7.
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Which of the following is a hierarchical listing of measurement scales in terms of increasing power? |
| (a) Nominal, interval, ordinal, ratio | |
| (b) Ordinal, nominal, ratio, interval | |
| (c) Nominal, ordinal, interval, ratio | |
| (d) Nominal, ordinal, ratio, interval | |
| (e) None of these. | |
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8.
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A stratified sample is of greatest statistical efficiency when |
| (a) the variances within strata are large. | |
| (b) the variances within strata are small. | |
| (c) the sample is a significant portion of the population. | |
| (d) the sample is large. | |
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9.
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One-sample tests are used in which of the following situations? |
| (a) Is there a difference between observed and expected proportions? | |
| (b) Is there a significant difference between a sample statistic and its population parameter? | |
| (c) Is it reasonable to conclude that a sample is drawn form a population with a specified distribution? | |
| (d) All the above. | |
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10.
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Suppose you calculate a correlation between age of head of household and household income. You find a correlation coefficient of |
| 0.55. Approximately what percent of income is "explained" by age? | |
| (a) About 74%. | |
| (b) About 55%. | |
| (c) About 30%. | |
| (d) Unknowable from information given. | |
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11.
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Analysis of Variance (ANOVA) is NOT used when |
| (a) the samples are not independent. | |
| (b) the dependent variable is continuous. | |
| (c) the samples are randomly selected. | |
| (d) many independent samples (three or more are involved). | |
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12.
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A larger standard deviation of a normal distribution indicates that the distribution becomes |
| (a) narrower and more peaked | |
| (b) flatter and wider | |
| (c) more skewed to the right | |
| (d) more skewed to the left. | |
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13.
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Which of the following is not a required condition for one-way ANOVA? |
| (a) The sample sizes must be equal | |
| (b) The populations must all be normally distributed | |
| (c) The population variances must be equal. | |
| (d) The samples for each treatment must be selected randomly and independently. | |
|
14.
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The primary interest of designing a randomized block experiment is to |
| (a) reduce the variation among blocks. | |
| (b) increase the between-treatments variation to more easily detect differences among the treatment means. | |
| (c) increase the total sum of squares. | |
| (d) reduce the within-treatments variation to more easily detect differences among the treatment means. | |
|
15.
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The ratio of two independent chi-squared variables divided by their degrees of freedom is |
| (a) normally distributed. | |
| (b) student t distributed. | |
| (c) F distributed. | |
| (d) chi-square distributed. | |
|
II.
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True-and-False Questions (30 points, 3 points for each. You should CORRECT the false statements in order to have credit.) |
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1.
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Methods of exploratory data analysis (EDA) are considered modern approaches to evaluating large batches of data. |
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2.
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The coefficient of variation is measured in the same units as are the original data value. |
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3.
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Histograms are horizontal bar charts. |
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4.
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Mutually exclusive events sum to one. |
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5.
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The binomial distribution will be symmetric when p=0.1 . |
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6.
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A sampling distribution is a probability distribution for a statistic. |
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7.
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A prediction interval is used to estimate a population parameter. |
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8.
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A dummy variable is used as an independent variable in a regression model when the variable involved is quantitative. |
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9.
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A regression diagnostic tool used to study the possible effects of multicollinearity is the variance inflationary factor (VIF). |
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10.
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The t-test for the significance of the slope in multiple regression is equivalent to a test for the significance of a set of independent |
| variables. | |
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III.
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Essay Questions: (25 points) |
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1.
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(a) What is a type I error? Can it be controlled? Why or why not? (5 points) |
| (b) What is a type II error? Can it be controlled? Why or why not? (5 points) | |
| (c) What is the p-value of a test? (5 points) | |
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2.
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Describe the statistical procedures when testing whether or not a new observation comes from the same population. (10 points) |
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