101年國立中山大學企業管理所(甲班丙班)統計學

A histogram is

a graphical presentation of a frequency or relative frequency distribution

a graphical method of presenting a cumulative frequency or a cumulative relative
frequency distribution

the history of data elements

the same as a pie chart

In a cumulative percent frequency distribution, the last class will have a cumulative
percent frequency equal to

One

100

the total number of elements in the data set

None of these alternatives is correct.

The sum of deviations of the individual data elements from their mean is

always greater than zero

always less than zero

sometimes greater than and sometimes less than zero, depending on the data
elements

always equal to zero

The numerical value of the variance

is always larger than the numerical value of the standard deviation

is always smaller than the numerical value of the standard deviation

is negative if the mean is negative

can be larger of smaller than the numerical value of the standard deviation

The variance of a sample was reported to be 144. The report indicated that
Σ(x − x)2 = 7200 . What has been the sample size?

49

50

51

52

If P(A) = 0.45 , P(B) = 0.55 , and P(AU B) = 0.78 , then P(A | B) =

zero

0.45

0.22

0.40

0.26 and 5.77

0.26 and 0.577

0.26 and 0.01

0 and 0.8

Twenty percent of the students in a class of 100 are planning to go to graduate school.
The standard deviation of this binomial distribution is

20

16

4

2

A production process produces 2% defective parts. A sample of five parts from the
production process is selected. What is the probability that the sample contains exactly
two defective parts?

0.0004

0.0038

0.10

0.02

For a continuous random variable X, the probability density function f (x) represents

the probability at a given value of x

the area under the curve at x

the area under the curve to the right of x

the height of the function at x

When a continuous probability distribution is used to approximate a discrete
probability distribution

a value of 0.5 is added and/or subtracted from the area

a value of 0.5 is added and/or subtracted from the value of x

a value of 0.5 is added to the area

a value of 0.5 is subtracted from the area

Z is a standard normal random variable. Not using Z-table, P(−1≤ Z ≤1) can be
judged to be closest to

0.8942

0.0558

0.675

0.7192

X is a normally distributed random variable with a mean of 20 and a standard
deviation of 4. Not using Z-table, the probability that X greater than or equal to 28 is
approximately

0.044

0.055

0.022

0.033

Sampling distribution of x is the

probability distribution of the sample mean

probability distribution of the sample proportion

mean of the sample

mean of the population

The standard deviation of a sample of 100 elements taken from a very large population
is determined to be 60. The variance of the population

can not be larger than 60

can not be larger than 3600

must be at least 100

can be any value greater or equal to zero

A theorem that allows us to use the normal probability distribution to approximate the
sampling distribution of sample means and sample proportions whenever the sample
size is large is know as the

approximation theorem

normal probability theorem

central limit theorem

central normality theorem

Random samples of size 81 are taken form an infinite population whose mean and
standard deviation are 200 and 18, respectively. The distribution of the population is
unknown. The mean and the standard error of the mean are

200 and 18

81 and 18

9 and 2

200 and 2

Random samples of size 525 are taken from an infinite population whose population
proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard
error of the proportion) is

0.0004

0.2100

0.3000

0.0200

The absolute value of the difference between the point estimate and the population
parameter it estimates is

the standard error

the sampling error

the margin of error

the error of confidence

A population has a standard deviation of 50. A random sample of 100 items from this
population is selected. The sample mean is determined to be 600. At 95% confidence,
not using Z-table, the margin of error can be found to be

5

9.8

650

609.8

For which of the following values of p (population proportion) is the value of
p(1− p) maximized?

p = 0.99

p = 0.90

p = 0.01

p = 0.50

Using α = 0.04 , a confidence interval for a population proportion is determined to be
0.65 to 0.75. If the level of significance is decreased, the interval for the population
proportion

becomes narrower

becomes wider

does not change

remains the same

Whenever using the t distribution for interval estimation (when the sample size is very
small), we must assume that

the sample has a mean of at least 30

the sampling distribution is not normal

the population is approximately normal

the finite population correction factor is necessary

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95%
confidence interval of voters not favoring the incumbent is

0.871 to 0.929

0.120 to 0.280

0.765 to 0.835

0.071 to 0.129

In hypothesis testing, the sum of the values of α and β

always add up to 1.0

always add up to 0.5

is the probability of Type II error

None of these alternatives is correct.

The p-value is a probability that measures the support for the

null hypothesis

alternative hypothesis

either the null or the alternative hypothesis

sample statistic

In order to test the following hypotheses at an α level of significance 0 : 800 H μ ≤
vs. Ha :μ > 800 the null hypothesis will be rejected if the test statistic Z is

≥ Za

< Za

< −Za

= Za

If a hypothesis is rejected at the 5% level of significance, it

will always be rejected at the 1% level

will always be accepted at the 1% level

will never be tested at the 1% level

may be rejected or not rejected at the 1% level

The average manufacturing work week in metropolitan Chattanooga was 40.1 hours
last year. It is believed that the recession has led to a reduction in the average work
week. To test the validity of this belief, the hypotheses are

H0 :μ < 40.1  vs. Ha :μ ≧40.1

H0 :μ  ≧40.1 vs.Ha :μ < 40.1

H0 :μ> 40.1  vs. Ha :μ ≦40.1

H0 :μ = 40.1  vs. Ha :μ ≠ 40.1

n = 64 x = 50 s = 16 0 :μ H ≧54 Ha :μ < 54 The test statistic equals

-4

-3

-2

+2

To compute an interval estimate for the difference between the means of two
populations, the t distribution

is restricted to small sample situations

is not restricted to small sample situations

can be applied when the populations have equal means

None of these alternatives is correct.

4

7.46

4.24

2.0

0.098

1.645

2.75

3.01

Referring to problem (33), the p-value is judged closest to

0.0013

0.0026

0.0042

0.0084

To avoid the problem of not having access to tables of the F distribution with values
given for the lower tail when a two-tailed test is required, let the smaller sample
variance be

the denominator of the test statistic

the numerator of the test statistic

at least one

None of these alternatives is correct.

The sampling distribution of the ratio of two independent sample variances taken from
normal populations with equal variances is

an F distribution

a Chi-Square distribution

a t distribution

a normal distribution

A sample of 60 items from population 1 has a sample variance of 8 while a sample of
40 items from population 2 has a sample variance of 10. If we test whether the
variances of the two populations are equal, the test statistic will have a value of

0.8

1.56

1.5

1.25

A goodness of fit test is always conducted as a

lower-tail test

upper-tail test

middle test

None of these alternatives is correct.

In order not to violate the requirements necessary to use the chi-square distribution,
each expected frequency in a goodness of fit test must be

at least 5

at least 10

no more than 5

less than 2

The degrees of freedom for a contingency table with 10 rows and 11 columns is

100

110

21

90

83

90

30

10

Referring to problem (41), the calculated value for the test statistic equals

0.5444

300

1.6615

6.6615

In factorial designs, the response produced when the treatments of one factor interact
with the treatments of another in influencing the response variable is know as

main effect

replication

interaction

None of these alternatives is correct.

An ANOVA procedure is applied to data obtained from 6 samples each sample
contains 20 observations. The degrees of freedom for the critical value of F are

6 numerator and 20 denominator degrees of freedom

5 numerator and 20 denominator degrees of freedom

5 numerator and 114 denominator degrees of freedom

6 numerator and 20 denominator degrees of freedom

μ1 = μ2 = μ3 = μ4

μ1 = μ2 = μ3 = μ4 = μ5

μ1 = μ2 = μ3 = μ4 = μ5 = μ6

μ1 = μ2 = ... = μ20

Referring to problem (45), the sum of squares due to error equals

14.4

2,073.6

5,760

6,000

Referring to problem (45), the test statistic to test null hypothesis equals

0.432

1.8

4.17

28.8

In a regression analysis, the coefficient of determination is 0.4225. The coefficient of
correlation in this situation is

0.65

0.1785

any positive value

any value

1

2

3

4

Referring to problem (49), the MSE is

1

2

3

4