生物统计与试验设计测验卷

浙江大学2010–2011学年秋冬学期

《Biostatistics and Experiment Design 》课程期中考试试卷

开课学院：农业与生物技术学院，考试形式：开卷，允许带 资料 入场 考试时间：2010年11月, 所需时间：120分钟

考生姓名： 学号： 专业：

题序 一 二 三 四 五 六 总 分 得分 评卷人

Question 1 (10 points)

1) In hypothesis testing, if the significance of statistical testing is α, the power is β, then, the

probability of type Ⅰerror is ，the probability of type Ⅱ error is.

2) For a population N (μ, σ2

), let X 1,X 2, ,X n is a sample from this population, then the population mean

μ can be estimated by the statistic , the population variance

can be estimated by the statistic .

Question 2 (10 points): For two random variables X 1~N (μ1, σ12

) and X 2~N (μ2, σ22

), their covariance is

ρ, let random vector x =

X

1

?X 2

()T

, y =X

2

X 1

()T

,

1) Write the equations for C xy and C yx

Question 3 (20 points): An experiment with 2 factors (A and B) is conducted with two replications, the levels of factor A and B is 3 and 2, respectively. The following fixed modelcan be applied in analysis:

Y ijk =μ+A

i

+B

j

+AB

ij

+e

ijk

,i=1,2,3;j=1,2;k=1,2;e ijk~N(0,σ2),Cov(e u,e′u)=0).

The model is expressed in matrix format y=Xb+e.

1)Write the matrix X,vector b, y and e

2)For the above menthioned vectors, define the constant vector and random vector.

3)Present equations for Var(e), Var(y) and Cov(y, e T).

4)What is relationship between general linear model and variance analysis model ?

Question 4 ( 20 points): The yield of a chemical process is related to the concentration of the reaction. An experiment has been conducted with the following results.

Yield 93.3 92.0 92.4 91.7 94.0 94.6 93.6 93.1 Concentration 1.10 1.45 1.36 1.59 1.08 0.75 1.20 0.99 Yield 93.2 92.9 92.2 91.3 90.1 91.6 91.9 Concentration 0.83 1.22 1.47 1.81 2.03 1.75 1.68

The output of SAS program for analysis is presented below:

1)Define the independent variable, dependent variable, parameter for the model, what are

distributions they follow.

2)Test the significance of regression.

3)Calculate the correlation coefficient between the independent variable and the dependent

variable.

4)Write out the formula for calculating the 95% confidence interval of regression parameter.

Question 5 (20 points): Suppose there is a non-linear relationship between the boll number of cotton per plant in different period (Y) and the number of days after the first blooming (X), which can be fitted by a

growth model: Y i=θ1exp[?θ2exp(?θ3X i)]+e i, the SAS program for analysis:

data nlincot;

input day boll @@;

cards;

5 0.75 10 2 15 4 20 4.7

6 25 5.25 30 5.5 35 7.75

40 10.13 45 12.26 50 13.14 55 13.52 60 14.15 65 14.53

;

proc nlin method=gauss;

parms a=2 b=1 c=0;

model boll=a*exp(-b*exp(-c*day));

run;

Some results of SAS for non-linear regression analysis are presented as follows:

1)Define parameter in non-linear regression model.

2)What is the method used in estimating the parameters, and what is the initial values of

parameters ?

3)What is your conclusion on the significance of the non-linear relationship ?

4)Test the significances of parameter.

Question 6 (20 points): In order to investigate the relationship between power consumption and family size, two regression models are applied in analyzing experiment data, the SAS program is as follows:

Data Dat;

input Power Home @@;

X1 = Home; X2 = Home * Home;

Datalines;

1182 1290 1172 1350 1264 1470 1493 1600 1571 1710 1711 1840

1804 1980 1840 2230 1956 2400 1954 2930

;

Proc REG;

Model Power = X1;

Run;

Proc REG;

Model Power = X1 X2;

Run;

1)Write out regression equations for two models, respectively.

2)Which model is better to reflect the relationship of power consumption and family size? Why?