统计学考试试题及答案

EXAMINATION OF ENVIRONMENTAL STATISTICS (A)

FOR UNDERGRADUATE STUDENTS MAJORING IN ENVIRONMENTAL SCIENCES

(THE FIRST SEMESTER OF THE ACADEMIC YEAR 2005 2006)

ID number

Class: Name:

Part one: Basic knowledge (40%; 5 points for each) 1. Population and sample

2. How to sample from populations?

3. How to show the dispersion or variability of a given set of data?

4. What are the basic assumptions that should be met when using parametric analyses? 5. What are statistical hypotheses? (Please also give an example)

6. What are the general procedures for ANCOVA (analysis of covariance)?

7. What are the statistical errors (Please show the difference between Type I and Type

II errors)?

8. The normal distribution

Part two: Statistical analyses (60%)

1. (7 points) The following sample data are on the length of the menstrual cycle in a

random sample of human females (N = 15):

26, 24, 29, 33, 25, 26, 23, 30, 28, 27, 29, 26, 31, 27 and 28 days

Please use one-sample t-test to test for the hypothesis that the mean length of human menstrual cycles is equal to a lunar month (a lunar month is 29.5 days). Please note that the two-tailed critical t value is 2.14 when P = 0.05 and df= 14.

2. (10 points) The Mann-Whitney test for ordinal data (The performance of students is

the same under the two teaching assistants). Please complete the following Table with tied ranks by filling the parentheses, and then test for whether the performance

3. (7 points) The following sample data are recorded as the observed frequencies (O),

by which you may use to test: H0: The sample comes from a population having a 3: 1 color pattern of pink to white flowers; HA: The sample comes from a population not having a 3: 1 ratio of the above two flower phenotypes. You are asked: (1) to show the expected frequencies (E), (2) to decide the trueness of the null hypothesis (H0) using Chi-square goodness of fit (X2 test) and Log-likelihood ratio (G-test).

4. The appendix is a set of data on female reproductive traits of five species of animals.

You are asked to re-arrange this dataset so that you will be able to do the following statistical analyses.

(10 points) Please use one-factor ANCOVA (with Species as the factor and SVL as

the covariate) to fill the following table and then compare the adjusted means of HL

Appendix: (SVL: Snout-vent length in mm; HL: Head length in mm; HW: Head width in mm; and BM: Body mass in gram)

SVL 66.66 60.54 63.13 61.96 63.14 59.33 67.91 58.87 63.88 60.5 61.27

HL 12.43 11.39 11.95 11.44 11.93 11.45 12.63 11.24 12.05 11.15 11.37

HW 7.48 7.13 7.36 7.18 6.93 6.75 7.71 7.04 7.76 6.86 7.29

BM 4.9246 3.9959 3.6596 4.2602 3.8593 3.0211 5.5102 3.4999 4.3147 4.0443 4.1152

Species 3SVL 58.2 66.63 65.34 60.76 60.59 61.45 60.14 67.34 62.1 64.5 59.42 68.31 56.51 HL 12 13.14 12.9 12.12 12.35 12.25 12.17 12.96 12.19 13.1 11.58 13.37 11.55 HW 7.88 8.52 8.51 8.18 7.56 7.37 7.62 8.48 8.2 8.1 7.45 8.44 7.17 BM 2.7544 5.6417 5.105 3.9593 3.8105 3.8932 3.7859 4.6012 4.3664 4.2695 4.2731 5.5003 3.6814

Species 4SVL 57.46 65.21 60.57 58.18 62.16 57.42 61.02 64.14 61.32 55.25 58.16 HL 12.07 13.61 13.13 13.02 12.85 12.56 12.97 12.77 13.32 11.97 13.1 HW 8.88 9.19 9.03 9.32 9.34 8.75 8.71 9.34 9.39 8.76 8.48 BM 4.334 5.776 3.961 5.005 4.508 4.324 4.597 5.031 5.561 4.126 3.407

59.17 59.63 56.38 55.41 57.64 60.92 59.92 61.97 58.73 53.02 59.55 58.49 61.78 59.16 57.42

12.74 12.62 12.83 12.19 12.14 13.54 12.76 13.35 13.13 11.89 13.15 12.44 13.59 13.29 12.61

9.05 8.72 8.83 8.18 8.69 9.02 8.35 8.71 7.63 8 8.1 8.62 8.01 8.19 7.99

3.899 3.564 4.095 3.597 4.055 4.666 4.16 5.728 4.835 3.967 4.355 4.463 4.556 4.14 3.769

Species 5SVL 53.5 55.44833 56.615 57.38 58.388 59.60407 60.55385 61.604 62.59048 63.57 64.47139 65.35667 66.27389 67.7375 68.155 70.51667 HL 10.73 11.77333 12.19 12.21714 12.21 12.34333 12.67462 12.77667 12.86571 12.93167 13.22333 13.52714 13.46238 13.92 13.95 14.03 HW 7.3 7.49 7.505 7.92 7.879 8.058889 8.104615 8.410667 8.333571 8.365 8.403333 8.525714 8.671905 9.03 9.09 8.96 BM 2.78 2.904 3.536 3.124286 3.2897 3.460037 3.660077 3.8278 3.880762 3.758917 4.239528 4.269286 4.295262 5.23625 4.317 4.793333