Description
In this collection there will be a bunch of various questions which concern all Economics, Mathematics, Computing and Business Students or any student who is interested in statistics
Study Set Content:
BASIC STATISTICS SELF TEST
1.
A researcher is interested in the travel time of Utrecht University students to college. A
group of 50 students is interviewed. Their mean travel time in 16.7 minutes. For this study
the mean of 16.7 minutes is an example of a(n)
A.
Parameter
B.
Statistic
C.
Population
D.
Sample
2.
A researcher is curious about the IQ of students at the Utrecht University. The entire group
students is an example of a:
A.
Parameter
B.
Statistic
C.
Population
D.
Sample
3.
Statistical techniques that summarize and organize the data are classified as:
A.
Population statistics
B.
Sample statistics
C.
Descriptive statistics
D.
Inferential statistics
4.
A sports psychologist was interested in the effects of a six-week imagery intervention on an
athlete’s ability to execute a sport-specific skills such penalty taking in football. How might
you define the imagery variable?
A.
Independent variable
B.
Dependent variable
C.
Outcome variable
D.
Resultant variable
5.
Five-point Likert scales (
strongly disagree, disagree, neutral, agree, strongly agree
) are
frequently used to measure motivations and attitudes. A Likert scale is a:
A.
Discrete variable.
B.
Ordinal variable.
C.
Categorical variable.
D.
All of the above options (A, B and C)
6.
In a 500m speed skating race, time results would be considered an example of which level of
measurement?
A.
Nominal
B.
Ordinal
C.
Interval
D.
Ratio
7.
IQ tests are standardized so that the mean score is 100 for the entire group of people who
take the test. However, if you select a group of 50 who took the test, you probably would
not get 100. What statistical concept explains the difference between the two means?
A.
Statistical error
B.
Inferential error
C.
Residual error
D.
Sampling error
8.
A researchers studies the factors that determine the number of children future couples
decide to have. The variable ‘number of children’ is a :
A.
Discrete variable
B.
Continuous variable
C.
Categorical variable
D.
Ordinal variable
9.
A teacher asks students to identity their favorite reality television show. What type of
measurement scale do the different television shows make up?
A.
Nominal
B.
Ordinal
C.
Interval
D.
Ratio
10.
The median is always:
A.
The most frequently occurring score in a data set
B.
The middle score when results are ranked in order of magnitude
C.
The same as the mean
D.
The difference between the maximum and minimum scores.
11.
The seminar rooms in the library are identified by the letters A to H. A researcher records
the number of classes held in each room during the first semester. What kind of graph
would be appropriate to present the frequency distributions of these data?
A.
Histogram
B.
Scatterplot
C.
Bar chart
D.
Box plot
12.
A set of scores is presented in a histogram. The histogram shows a series of bars that tend
to decrease in height from left to right. What is the shape of the distribution?
A.
Leptokurtic
B.
Positively skewed
C.
Negativity skewed
D.
Normal
13.
What is the mean for the following scores: 2, 5, 4, 1, 8?
A.
3
B.
4
C.
5
D.
20
14.
What is the mean for the scores shown in the frequency distribution?
A.
1.5
B.
3.0
C.
2.9
D.
5.8
15.
What is the median for the following scores: 2, 5, 4, 1, 8?
A.
3.5
B.
4
C.
4.5
D.
7
16.
A teacher gave a statistics test to a class of Geography students and computed the measures
of central tendency for the test scores. Which of the following statements cannot be an
accurate description of the scores?
A.
The majority of students had scores above the mean.
B.
The majority of students had scores above the median.
C.
The majority of students had scores above the mode.
D.
All of the above options (A, B and C) are false statements.
17.
Which of the following sets of scores has the greatest variability ( range)?
A.
2, 5, 8, 11
B.
13, 13, 13, 13
C.
20, 25, 26 ,27
D.
42, 43, 44, 45
18.
Which of the following statements is the most accurate description for the concept of
standard deviation?
A.
The total distance from the smallest score to the highest score.
B.
The square root of the total distance from the smallest score to the highest score.
C.
The squared average distance between all scores and the mean.
D.
The average distance between a score and the mean.
19.
What is the variance for the following set of scores: 2, 2, 2, 2, 2.
A.
0
B.
2
C.
4
D.
25
Value
f
1
1
2
3
3
3
4
2
5
1
20.
Normally distributed data are normally referred to as:
A.
Bell-shaped
B.
Asymmetrical
C.
Skewed
D.
Peaked
21.
Take the formula Z = (X – µ)/σ, where µ is the mean of the population, X is the value of the
element, Z is the z-score and σ is the standard deviation. What does this formula calculate?
A.
Confidence interval.
B.
Standard score.
C.
Standard error of the mean.
D.
Variance.
22.
A population has a mean of μ=35 and a standard deviation of σ=5. After 3 points are added
to every score in the population, what are the new values for the mean and standard
deviation?
A.
μ=35 and σ=5
B.
μ=35 and σ=8
C.
μ=38 and σ=5
D.
μ=38 and σ=8
23.
Of the following Z-score values, which one represents the location closest to the mean?
A.
Z=+0.5
B.
Z=+1,0
C.
Z=-1.5
D.
Z=-0.3
24.
If the scores on a test have a mean of 26 and a standard deviation of 4, what is the
z
-score
for a score of 18?
A.
2
B.
11
C.
-2
D.
–1.41
25.
A population has a μ=50 and σ=10. If these scores are transformed into z-scores, the
population of z-scores will have a mean and standard deviation of:
A.
μ=50 and σ=10
B.
μ=50 and σ=1,96
C.
μ=1 and σ=0
D.
μ=0 and σ=1
26.
If all possible samples of size n=30 are selected from a population with μ=80 and σ=10 and
the mean is computed for each sample, then what shape is expected for the distribution of
sample means?
A.
The sample means tend to form a normal-shaped distribution whether the
population is normal or not.
B.
The sample means tend to form a normal-shaped distribution only if the population
distribution is normal.
C.
The sample size of n=30 is too small to predict the shape of the distribution.
D.
The mean of each sample will be very close to 80, hence the distribution of means
will have little variability.
27.
What is a definition of the standard error?
A.
Standard deviation of the sample.
B.
Squared standard deviation.
C.
Standard deviation of sample means.
D.
Standard deviation of the population mean.
28.
If a researcher sets a level of significance at .05 (i.e. 5%), what does this mean?
A.
Five times out of 100, a significant result will be found that is due to chance alone
and not to true relationship.
B.
Ninety-five times out of 100, a significant result will be found that is due to chance
alone and not to true relationship.
C.
Five times out of 100, a significant result will be found that is not due to chance, but
to true relationship.
D.
None of the above.
29.
When does a researcher risk a Type I error?
A.
Anytime the decision is ‘fail to reject’.
B.
Anytime H
0
is rejected.
C.
Anytime H
1
is rejected.
D.
All of the above options.
30.
Which of the following assumptions are required if an independent t-test is to be used?
A.
Samples are drawn from a normally distributed population.
B.
Homogeneity of variances (equal variances).
C.
The data are either interval or ratio scales.
D.
All the above assumptions (A, B and C) are required.
31.
What is the correct decision in a hypothesis if the data produce a t-statistic that is in the
critical region?
A.
Reject H
0
B.
Fail to reject H
0
C.
Reject H
1
D.
Fail to reject H
1
32.
How does the shape of the t distribution compare to the normal distribution?
A.
The t distribution is taller and less spread out, especially when n is large.
B.
The t distribution is taller and less spread out, especially when n is small.
C.
The t distribution is flatter and more spread out, especially when n is large.
D.
The t distribution is flatter and more spread out, especially when n is small.
33.
Suppose you wanted to apply a one-tailed test as opposed to a two-tailed test. How would
you covert a significance of p = .284?
A.
.
284 / 2 = .142
B.
.284 × 2 = .568
C.
.284 / 0.05 = 5.68
D.
.284 × 0.05 = .0142
34.
A research report summarizes the results of a t-test by stating:
t(35)=5.2, p<0.05
.
Which of the following is a correct interpretation of this report?
A.
The H
0
was not rejected and the probability of a Type I error is less than .05.
B.
The H
0
was not rejected and the probability of a Type II error is less than .05.
C.
The H
0
was rejected and the probability of a Type I error is less than .05.
D.
The H
0
was rejected and the probability of a Type II error is less than .05.
35.
Which of the following is true about a 95% confidence interval of the mean of a given
sample:
A.
95 out of 100 sample means will fall within the limits of the confidence interval.
B.
There is a 95% chance that the population mean will fall within the limits of the
confidence interval.
C.
95 out of 100 population means will fall within the limits of the confidence interval.
D.
There is a .05 probability that the population mean falls within the limits of the
confidence interval.
36.
What effect would increasing the sample size have on a confidence interval?
A.
The confidence interval would increase in size.
B.
The confidence interval would decrease in size.
C.
The confidence interval is unaffected by sample size.
D.
The confidence interval could either increase or decrease in size.
37.
In an independent
t
-test output of SPSS, the Levene’s test result is
p
= .006. What can we
infer from this number?
A.
The means of both groups are assumed to be unequal.
B.
The means of both groups are assumed to be equal.
C.
The variances of both groups are assumed to be unequal.
D.
The variances of both groups are assumed to be equal.
38.
What does ANOVA stand for?
A.
Analysis of values and averages.
B.
Analysis of variance.
C.
Analysis of variability.
D.
Analysis of non ordinal values.
39.
What kind of variables would you crosstabulate?
A.
Two or more categorical.
B.
Two or more continuous.
C.
One continuous and two or more categorical.
D.
One categorical and two or more continuous.
40.
Which statistical test is used to identify whether there is a relationship between two
categorical variables?
A.
Student’s t-test.
B.
Spearman’s correlation test.
C.
Pearson’s Chi-square test.
D.
Mann-Whitney test.
41.
What does the statistic Cramer’s V indicate?
A.
The significance of the Chi-square test.
B.
The expected frequencies in a contingency table.
C.
The amount of common variability of two numeric variables.
D.
The strength of association between two categorical variables..
42.
What is the null hypothesis for a Chi-square test?
A.
Both variables have a significant relationship.
B.
Both variables have equal means.
C.
Both variables are independent.
D.
Both variables are dependent.
43.
In order for accurate measures of the linear relationship between two variables to be
achieved, what type of data are required if using Pearson’s correlation coefficient?
A.
Nominal
B.
Ordinal
C.
Interval
D.
Ratio
44.
A Pearson correlation of r=-0.6 indicates
A.
An increase in X is accompanied by an increase in Y; the relationship is strong.
B.
An increase in X is accompanied by an increase in Y; the relationship is moderate.
C.
An increase in X is accompanied by a decrease in Y; the relationship is strong.
D.
An increase in X is accompanied by a decrease in Y; the relationship is moderate.
45.
2. A scatterplot shows:
A.
The frequency with which values appear in the data.
B.
The average value of groups of data.
C.
Scores on one variable plotted against scores on a second variable.
D.
The proportion of data falling into different categories.
46.
R
2
is the notation for:
A.
The coefficient of correlation.
B.
The coefficient of determination.
C.
The coefficient of variation.
D.
The coefficient of regression.
47.
Suppose the correlation between height and weight for adults is +0.80. What proportion of
the variability in weight can be explained by the relationship with height?
A.
20%
B.
36%
C.
64%
D.
80%
48.
In a linear regression equation, Y=a + bX, what is the b denote?
A.
The regression coefficient, the slope of the line.
B.
The intercept with the Y-axis.
C.
The correlation coefficient, the strength of the line
D.
The score on the variable X.
49.
In a linear regression equation, what does a slope of 2.5 indicate?
A.
For every increase of 2.5 on the y-axis, there is an increase of 5.0 on the x-axis.
B.
For every increase of 2.5 on the x-axis, there is an equivalent increase on the y-axis.
C.
For every increase of 1.00 on the x-axis, there is an increase of 2.5 on the y-axis.
D.
For every increase of 1.00 on the y-axis, there is an decrease of 2.5 on the x-axis.
50.
Which of the following statements about the t-statistic in regression analysis is not true?
A.
The t-statistic tests whether the regression coefficient, b, is equal to 0.
B.
The t-statistic provides some idea of how well a predictor predicts the outcome
variable.
C.
The t-statistic can be used to see whether a predictor variable makes a statistically
significant contribution to the regression model.
D.
The t-statistic is equal to the regression coefficient divided by its standard deviation.
ANSWERS
1
B
11
C
21
B
31
A
41
D
2
C
12
B
22
C
32
D
42
C
3
C
13
B
23
D
33
A
43
C
4
A
14
C
24
C
34
C
44
D
5
D
15
B
25
D
35
B
45
C
6
D
16
B
26
A
36
B
46
B
7
D
17
A
27
C
37
D
47
C
8
A
18
D
28
A
38
B
48
A
9
A
19
A
29
B
39
A
49
C
10
B
20
A
30
D
40
C
50
D
RESULTS
correct ansewers:
40-50 good
basic statistical knowledge meets expectations
30-40 satisfactory
acceptable level of knowledge
20-30 unsatisfactory
some improvement required; reading Field* recommended.
<20
poor
basic knowledge inadequate; reading Field* necessary.
*
Andy Field, Discovering Statistics using SPSS. 4th ed. Chapt. 1-3; 7.4-7.4.2; 8.1-8.4; 9.1-9.5.
Sample Statistics Exam #500
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
1. Which is the following is correct?
a. The probability of a type I error is
β
.
b. The probability of a type II error is (1 -
β
).
c. The probability of a type II error is
α.
d. The probability of a type I error is (1 -
α
).
e. none of the above
2. A random sample of 10 items is taken from a normal population. The sample had a mean of 82 and a
standard deviation is 26. Which is the appropriate 99% confidence interval for the population mean?
a.
b.
c.
d.
e. none of the above
3. A manufacturer of contact lenses is studying the curvature of the lenses it sells. In particular, the last 500
lenses sold had an average curvature of 0.5. The population is
a. the 500 lenses.
b. 0.5.
c. the lenses sold today.
d. all the lenses sold by the manufacturer.
e. none of the above
4. According to the empirical rule, the bell or mound shaped distribution will have approximately 68% of the
data within what number of standard deviations of the mean?
a. one
standard
deviation
b. two standard deviations
c. three standard deviations
d. four
standard
deviations
e. none of the above
5. A random sample of 5 mosquitos is sampled. The number of mosquitos carrying the West Nile Virus in the
sample is an example of which random variable?
a. normal
b. student’s
t
c. binomial
d. uniform
e. none of the above
6. A political scientist is studying voters in California. It is appropriate for him to use a mean to describe
a. the age of a typical voter.
b. the party affiliation of a typical voter.
c. the sex of a typical voter.
d. the county of residence of a typical voter.
e. none of the above
7. The long-run average of a random variable is
a. the expected value
b. the coefficient of determination
c. the standard deviation
d. the
mode
e. none of the above
8. A manufacturer of women’s blouses has noticed that 80% of their blouses have no flaws, 15% of their blouses
have one flaw, and 5% have two flaws. If you buy a new blouse from this manufacturer, the expected number
of flaws will be
a. 0.15
b. 0.20
c. 0.80
d. 1.00
e. none of the above
9. If population A has a larger standard deviation than population B, which of the following is NOT true?
a. Population B has a smaller variance than population A.
b. The mean of a sample of 20 from population A has a larger standard deviation than the
mean of a sample of 20 from population B.
c. A typical observation from population A will be farther from the mean of population A
than a typical observation from B will be from the mean of population B.
d. The mean of a sample from population A will on average be larger than the mean of a
sample from population B.
e. none of the above
10. An inspector needs to learn if customers are getting fewer ounces of a soft drink than the 28 ounces stated on
the label. After she collects data from a sample of bottles, she is going to conduct a test of a hypothesis. She
should use
a. a two tailed test.
b. a one tailed test with an alternative to the right.
c. a one tailed test with an alternative to the left.
d. either a one or a two tailed test because they are equivalent.
e. none of the above
11. The manufacturer of Anthony Big’s exercise equipment is interested in the relationship between the number
of months (X) since the equipment was purchased by a customer and the number of hours (Y) the customer
used the equipment last week. The result was the regression equation Y = 12 - 0.5X. The number 0.5 in the
equation means that the average customer
a. used the equipment for 30 minutes last week.
b. who has owned the equipment an extra month used the equipment 30 minutes less last
week than the average customer who has owned it one month less.
c. who just bought the equipment used it 30 minutes last week.
d. bought the equipment one-half month ago.
e. none of the above
12. A researcher is studying students in college in California. She takes a sample of 400 students from 10
colleges. The average age of all college students in California is
a. a
statistic.
b. a
parameter.
c. the
median.
d. a
population.
e. none of the above
13. A sample of 150 new cell phones produced by Yeskia found that 12 had cosmetic flaws. A 90% confidence
interval for the proportion of all new Yeskia phones with cosmetic flaws is 0.044 to 0.116. Which statement
below provides the correct interpretation of this confidence interval?
a. There is a 90% chance that the proportion of new phones that have cosmetic flaws is
between 0.044 and 0.116.
b. There is at least a 4.4% chance that a new phone will have a cosmetic flaw.
c. A sample of 150 phones will have no more than 11.6% with cosmetic flaws.
d. If you selected a very large number of samples and constructed a confidence interval for
each, 90% of these intervals would include the proportion of all new phones with cosmetic
flaws.
e. none of the above
14. The standard deviation of a normal population is 10. You take a sample of 25 items from this population and
compute a 95% confidence interval. In order to compute the confidence interval, you will use
a. the t table because the degrees of freedom will be 24.
b. the t table because you have estimated the standard deviation from the sample.
c. the z table because the population standard deviation is known.
d. the z table because the sample size is small.
e. none of the above
15. You are conducting a one-sided test of the null hypothesis that the population mean is 532 versus the
alternative that the population mean is less than 532. If the sample mean is 529 and the p-value is 0.01, which
of the following statements is true?
a. There is a 0.01 probability that the population mean is smaller than 529.
b. The probability of observing a sample mean smaller than 529 when the population mean is
532 is 0.01.
c. There is a 0.01 probability that the population mean is smaller than 532.
d. If the significance level is 0.05, you will accept the null hypothesis.
e. none of the above
16. Half of the observations in a data set are greater than the
a. mean.
b. median.
c. mode.
d. standard
deviation.
e. none of the above
Sample Statistics Exam #500
Answer Section
MULTIPLE CHOICE
1.
ANS:
E
DIF:
2
TOP:
2
2.
ANS:
D
DIF:
2
TOP:
3
3.
ANS:
D
DIF:
2
TOP:
9
4.
ANS:
A
DIF:
2
TOP:
1
5.
ANS:
C
DIF:
2
TOP:
6
6.
ANS:
A
DIF:
2
TOP:
10
7.
ANS:
A
DIF:
2
TOP:
5
8.
ANS:
E
DIF:
2
TOP:
5
9.
ANS:
D
DIF:
2
TOP:
8
10.
ANS:
C
DIF:
2
TOP:
2
11.
ANS:
B
DIF:
2
TOP:
4
12.
ANS:
B
DIF:
2
TOP:
9
13.
ANS:
D
DIF:
2
TOP:
3
14.
ANS:
C
DIF:
3
TOP:
6
15.
ANS:
B
DIF:
2
TOP:
7
16.
ANS:
B
DIF:
1
TOP:
1
