中原大學九十二學年度碩士班招生考試

中原大學九十二學年度碩士班招生考試

92年3月22日　16:00~17:30　資訊管理學系	誠實是我們珍視的美德，我們喜愛「拒絕作弊，堅守正直」的你！
科目：統計學

一、	選擇題（15題，每題2分，共30分）
1.	An unbiased estimate of the population total is given by the
	a.	sample mean multiplied by the size of the sample
	b.	sample mean multiplied by the size of the population
	c.	sample size multiplied by the standard error
	d.	standard deviation divided by the square root of the sample size
	e.	None of the above answers is correct.

2.	A version of cluster sampling in which the elements are formed into clusters on the basis of their geographic proximity is
	a.	area sampling
	b.	random sampling
	c.	judgment sampling
	d.	stratified simple random sampling
	e.	None of the above answers is correct.

3.	A list of the sampling units for a study is
	a.	the sampled population	b.	called the frame
	c.	the same as the sample	d.	the sample space
	e.	None of the above answers is correct.

4.	A nonparametric method for determining the differences between two populations based on two matched samples where only preference data is required is the
	a.	Mann-Whitney-Wilcoxon test	b.	Wilcoxon signed-rank test
	c.	sign test	d.	Kruskal-Wallis Test
	e.	None of the above answers is correct.

5.	Ten people were given two types of cereal, Brand X and Brand Y. 3 people preferred Brand X, 5 people preferred Brand Y, and 2 people were undecided. We want to determine whether or not the two products are equal. To test the null hypothesis, the appropriate probability distribution to use is
	a.	normal	b.	chi-square
	c.	Poisson	d.	binomial
	e.	None of the above answers is correct.

6.	A method that uses a weighted average of past values for arriving at smoothed time series values is known as
	a.	a smoothing average	b.	a moving average
	c.	an exponential average	d.	an exponential smoothing
	e.	None of the above answers is correct.

7.	In a regression model involving 30 observations, the following estimated regression equation was obtained. =170 + 34X₁ - 3X₂ + 8X₃ + 58X₄ + 3X₅ For this model, SSR = 1,740 and SST = 2,000. The degrees of freedom associated with SST are
	a.	24	b.	6
	c.	19	d.	5
	e.	None of the above answers is correct.

8.	In a multiple regression model, the variance of the error term ε is assumed to be
	a.	the same for all values of the dependent variable
	b.	zero
	c.	the same for all values of the independent variable
	d.	-1
	e.	None of the above answers is correct.

9.	In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is
	a.	0.65	b.	0.11
	c.	0.35	d.	0.81
	e.	None of the above answers is correct.

10.	In simple linear regression analysis, which of the following is not true?
	a.	The F test and the t test yield the same results.
	b.	The F test and the t test may or may not yield the same results.
	c.	The relationship between X and Y is represented a straight line.
	d.	The value of F = t2.
	e.	None of the above answers is correct.

11.	The ANOVA procedure is a statistical approach for determining whether or not the means of
	a.	two samples are equal
	b.	more than two samples are equal
	c.	two or more samples are equal
	d.	two or more populations are equal
	e.	All of the above answers are correct.

12.	A sample of n observations is taken from a population. The appropriate chi-square distribution has
	a.	n degrees of freedom	b.	n - 1 degrees of freedom
	c.	n - 2 degrees of freedom	d.	n - 3 degrees of freedom
	e.	None of the above answers is correct.

13.	If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error
	a.	will also increase from .01 to .05
	b.	will not change
	c.	will decrease
	d.	Not enough information is given to answer this question.
	e.	None of the above answers is correct.

14.	A graphical device used for enumerating sample points in a multiple-step experiment is a
	a.	bar chart	b.	pie chart
	c.	histogram
	d.	cumulative frequency distribution
	e.	None of the above answers is correct.

15.	Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.2. The complement of Event B equals
	a.	0.00	b.	0.06
	c.	0.7	d.	0.1
	e.	None of the above answers is correct.

二、

計算題(7題，共70分)

Thirty four observations of a dependent variable (Y), and two independent variables resulted in an SSE of 300. When a third independent variable was added to the model, the SSE was reduced to 250. At 95% confidence, determine if the third independent variable contributes significantly to the model.(10%)

Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained.
150 150 180 170

State the null and alternative hypotheses.(2%)

Using a standardized test statistic, test the hypothesis at the 10% level of significance.(3%)

Using a confidence interval, test the hypothesis at the 10% level of significance.(3%)

Compute the probability of a Type II error if the true running time of movies equals 130 minutes.(2%)

A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 10.

The professor has informed us that 16.6 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? (3%)

If 12.1 percent of her students failed the course and received F's, what was the maximum score among those who received an F? (3%)

If 33 percent of the students received grades of B or better (i.e., A's and B's), what is the minimum score of those who received a B? (4%)

Allied Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below.

Program A	Program B	Program C	Program D
150	150	185	175
130	120	220	150
120	135	190	120
180	160	180	130
145	110	175	175

Construct an ANOVA table.(5%)

As the statistical consultant to Allied, what would you advise them? Use α = 0.05 level of significance.(5%)

Use Fisher's LSD procedure and determine which population mean (if any) is different from the others. Let α= 0.05.(5%)

A retailer of electronic equipment received six VCRs from the manufacturer. Three of the VCRs were damaged in the shipment. The retailer sold two VCRs to two customers.

Can a binomial formula be used for the solution of the above problem?(2%)

What kind of probability distribution does the above satisfy, and is there a function for solving such problems?(2%)

What is the probability that both customers received damaged VCRs?(3%)

What is the probability that one of the two customers received a defective VCR?(3%)

A regression analysis was applied in order to determine the relationship between a dependent variable and 8 independent variables. The following information was obtained from the regression analysis.
R Square = 0.80 SSR = 4,280 Total number of observations n = 56

Fill in the blanks in the following ANOVA table.(5%)

Is the model significant? Let α = 0.05.(5%)

Source of

Degrees

Sum of

Mean

Variation

of Freedom

Squares

Regression

__________?

______?

_____?

Error

__________?

______?

_______________________________________________________________

Total

__________?

______?

The following data show the test scores of six individuals on a standardized test before and after attending a preparation seminar for the test.

Person	Before	After
A	108	110
B	102	118
C	107	105
D	97	97
E	112	116
F	108	106

Use Wilcoxon signed-rank test in order to determine whether or not the seminar has been effective. Hint: This is a one tailed test. Let α= 0.05. (5%)

三、

計算參考值

F(0.025; 1,18)=5.98	F(0.025; 1,30)=5.57	F(0.025; 1,40)=5.42
F(0.025; 2,17)=4.62	F(0.025; 2,30)=4.18	F(0.025; 2,40)=4.05
F(0.025; 3,16)=4.08	F(0.025; 4,15)=3.80	F(0.025; 8,40)=2.53
F(0.025; 8,60)=2.41	F(0.05; 1,18)=4.41	F(0.05; 1,30)=4.17
F(0.05; 1,40)=4.08	F(0.05; 2,17)=3.59	F(0.05; 2,30)=3.32
F(0.05; 2,40)=3.23	F(0.05; 3,16)=3.24	F(0.05; 4,15)=3.06
F(0.05; 8,40)=2.18	F(0.05; 8,60)=2.1
t(0.025,3)=3.182	t(0.025,4)=2.776	t(0.05,3)=2.353
t(0.05,4)=2.132

Z分配表

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