| I.選擇題 (15題，每題3分，共45分) |
| 1. |
A researcher has collected the sample data 5, 7, 14, 5, 4.
The mean of the sample is 7. The variance is |
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(a) |
8 |
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(b) |
4.062 |
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(c) |
13.2 |
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(d) |
16.5 |
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| 2. |
In the textile industry, a manufacturer is interested in
the number of blemishes or flaws occurring in each 10 feet of material.
The probability distribution that has the greatest chance of applying to
this situation is the |
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(a) |
normal distribution |
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(b) |
binomial distribution |
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(c) |
Poisson distribution |
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(d) |
uniform distribution |
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| 3. |
The random variable x is known to be uniformly distributed
between 50 and 70. The probability of x having a value between 65 to 75
is |
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(a) |
0.75 |
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(b) |
0.5 |
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(c) |
0.25 |
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(d) |
1 |
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| 4. |
A population has a standard deviation of 12. If a sample of
size 36 is selected from this population, what is the probability that the
sample mean will be within ±2 of the population mean? |
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(a) |
0.6826 |
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(b) |
0.3413 |
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(c) |
0.4772 |
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(d) |
Since the mean is not given, there is no answer to this question. |
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| 5. |
Given two unbiased point estimators of the same population
parameter, the point estimator with the smaller variance is said to have |
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(a) |
smaller relative efficiency |
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(b) |
greater relative efficiency |
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(c) |
smaller consistency |
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(d) |
larger consistency |
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| 6. |
The school's newspaper reported that the proportion of students
majoring in business is at least 30%. You plan on taking a sample to test
the newspaper's claim. The correct set of hypotheses is |
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(a) |
 |
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(b) |
 |
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(c) |
 |
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(d) |
 |
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| 7. |
If a hypothesis is rejected at the 5% level of significance,
it |
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(a) |
will always be rejected at the 1% level |
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(b) |
will always be accepted at the 1% level |
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(c) |
will never be tested at the 1% level |
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(d) |
may be rejected or not rejected at the 1% level |
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| 8. |
An important application of the chi-square distribution is |
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(a) |
making inferences about a single population variance |
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(b) |
testing for goodness of fit |
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(c) |
testing for the independence of two variables |
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(d) |
All of these alternatives are correct. |
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| 9. |
Correlation analysis is used to determine |
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(a) |
the equation of the regression line |
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(b) |
the strength of the relationship between the dependent and the independent
variables |
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(c) |
a specific value of the dependent variable for a given value of the independent
variable |
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(d) |
None of these alternatives is correct. |
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| 10. |
When multicollinearity exists |
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(a) |
it is indicated by a pattern in the residuals. |
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(b) |
the explanation of the causal effects of individual variables on y should
be undertaken with great caution. |
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(c) |
confidence interval estimates of the parameters are unaffected. |
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(d) |
the independent variables in the model must be independent from one another. |
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| 11. |
If two variables, x and y, have a good linear relationship,
then |
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(a) |
there may or may not be any causal relationship between x and y |
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(b) |
x causes y to happen |
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(c) |
y causes x to happen |
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(d) |
None of these alternatives is correct. |
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| 12. |
A variable such as Z, whose value is Z = X1X2 is added to
a general linear model in order to account for potential effects of two
variables X1 and X2 acting together. This type of effect is |
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(a) |
impossible to occur |
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(b) |
called interaction |
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(c) |
called multicollinearity effect |
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(d) |
called transformation effect |
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| 13. |
A nonparametric method for determining the differences between
two populations based on two matched samples where only preference data
is required is the |
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(a) |
Mann-Whitney-Wilcoxon test |
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(b) |
Wilcoxon signed-rank test |
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(c) |
sign test |
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(d) |
Kruskal-Wallis Test |
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| 14. |
A nonparametric test for the equivalence of two populations
would be used instead of a parametric test for the equivalence of the population
parameters if |
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(a) |
the samples are very large |
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(b) |
the samples are not independent |
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(c) |
no information about the populations is available |
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(d) |
The parametric test is always used in this situation. |
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| 15. |
The width of both the confidence interval for E(y｜x) and the
prediction of interval for y｜x become greater |
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(a) |
the smaller the standard deviation s. |
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(b) |
the greater the sample size n. |
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(c) |
the greater the variation of x. |
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(d) |
the greater the distance between the given value of x and the mean of
x. |
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| II.說明題 (3題，每題5分，共15分) |
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(a) |
What does it mean to say that two events are independent? |
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(b) |
Why is the sample standard deviation rather than the sample variance often
a more useful measure of variability? |
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(c) |
Describe the coefficient of variation. What advantage is offered by using
the coefficient of variation as a measure of variability instead of variance? |
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| III. |
A randomized block design was conducted to compare the means
of four treatments with five blocks. Suppose the analysis of variance calculations
gives SST = 12.1, SSB = 18.3, and Total SS = 41.5. |
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(a) |
Construct the ANOVA table. (5%) |
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(b) |
State the null and alternative hypotheses for an analysis of variance.
(2%) |
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(c) |
Give the rejection region for the test, part (b), for α = 0.05 and the
conclusion. (3%) |
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| IV. |
The monthly rent for a two-bedroom apartment in a particular
city is reported to average $550. Suppose we want to test 
A sample of 36 two-bedroom apartments is selected. The sample mean turns
out to be 
= $562, with a sample standard deviation of s = $40. |
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(a) |
Using a 0.05 level of significance, what is the rejection rule for this
test? (3%) |
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(b) |
What is your conclusion with α = 0.05? (2%) |
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(c) |
Compute the p-value. (5%) |
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(d) |
What is the probability of making a Type II error when μ = 560? (5%) |
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| V. |
Consider the following data for corresponding values of two
variables x and y: |
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x
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-4
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-2
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-1
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0
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3
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4
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y
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1.9
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2.1
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1.1
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1.2
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0.9
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0.6
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(a) |
Interpret the mean of the coefficient of correlation. (5%) |
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(b) |
Calculate the coefficient of correlation for this data and interpret this
value. (5%) |
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(c) |
By what percentage was the sum of squares of deviations reduced by using
the least squares predictor  ,
rather than the sample mean  ,
as an estimator of y? (5%) |
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計算參考值 |
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