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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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Subjects
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clep
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math
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Independent Selection
A Probability measure
Inferential
Cumulative distribution functions
2. Is a sample space over which a probability measure has been defined.
A probability space
Ordinal measurements
P-value
A data set
3. Statistical methods can be used for summarizing or describing a collection of data; this is called
descriptive statistics
A probability space
hypothesis
the sample or population mean
4. In number theory - scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns - which may then lead to
hypotheses
A sampling distribution
Ratio measurements
An event
5. A collection of events is mutually independent if for any subset of the collection - the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-fl
Statistics
Ordinal measurements
Mutual independence
Type II errors
6. Is a subset of the sample space - to which a probability can be assigned. For example - on rolling a die - 'getting a five or a six' is an event (with a probability of one third if the die is fair).
Conditional probability
the population mean
An event
Parameter
7. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Alpha value (Level of Significance)
A Distribution function
Probability density functions
Step 2 of a statistical experiment
8. Var[X] :
Probability density
Placebo effect
Interval measurements
variance of X
9. When there is an even number of values...
A population or statistical population
A probability space
That is the median value
The average - or arithmetic mean
10. Samples are drawn from two different populations such that there is a matching of the first sample data drawn and a corresponding data value in the second sample data.
Dependent Selection
Valid measure
A probability density function
Probability
11. Is used in 'mathematical statistics' (alternatively - 'statistical theory') to study the sampling distributions of sample statistics and - more generally - the properties of statistical procedures. The use of any statistical method is valid when the
Probability
Type I errors
Count data
A likelihood function
12. Probability of rejecting a true null hypothesis.
Binary data
Alpha value (Level of Significance)
Ordinal measurements
A population or statistical population
13. (cdfs) are denoted by upper case letters - e.g. F(x).
Average and arithmetic mean
The standard deviation
A data set
Cumulative distribution functions
14. Can be - for example - the possible outcomes of a dice roll (but it is not assigned a value). The distribution function of a random variable gives the probability of different results. We can also derive the mean and variance of a random variable.
the sample or population mean
Dependent Selection
A random variable
Type II errors
15. When you have two or more competing models - choose the simpler of the two models.
Qualitative variable
Law of Parsimony
Correlation coefficient
Interval measurements
16. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
Step 3 of a statistical experiment
Independence or Statistical independence
Conditional probability
17. Have both a meaningful zero value and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data
Ratio measurements
Bias
Step 1 of a statistical experiment
Lurking variable
18. Is the probability of two events occurring together. The joint probability of A and B is written P(A and B) or P(A - B).
hypotheses
Joint probability
Statistic
Mutual independence
19. Given two jointly distributed random variables X and Y - the marginal distribution of X is simply the probability distribution of X ignoring information about Y.
Variable
Inferential statistics
Marginal distribution
Law of Large Numbers
20. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
methods of least squares
P-value
Parameter
Type II errors
21. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Law of Large Numbers
Coefficient of determination
applied statistics
Descriptive
22. Changes over time that show a regular periodicity in the data where regular means over a fixed interval; the time between repetitions is called the period.
Sampling
A Random vector
the population mean
Seasonal effect
23. Many statistical methods seek to minimize the mean-squared error - and these are called
Credence
methods of least squares
inferential statistics
Block
24. Is a typed measurement - it can be a boolean value - a real number - a vector (in which case it's also called a data vector) - etc.
A data point
Independent Selection
Seasonal effect
Descriptive statistics
25. A numerical measure that describes an aspect of a population.
Parameter
variance of X
Variability
Conditional distribution
26. ?r
Skewness
A likelihood function
the population cumulants
Sampling Distribution
27. Data are gathered and correlations between predictors and response are investigated.
Law of Large Numbers
applied statistics
observational study
A statistic
28. Are two related but separate academic disciplines. Statistical analysis often uses probability distributions - and the two topics are often studied together. However - probability theory contains much that is of mostly of mathematical interest and no
Probability and statistics
The Covariance between two random variables X and Y - with expected values E(X) =
Individual
the population variance
29. Of a group of numbers is the center point of all those number values.
Correlation coefficient
The average - or arithmetic mean
Law of Large Numbers
Observational study
30. Summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types (like heights or weights) - while frequency and percentage are
The median value
Descriptive statistics
Simulation
expected value of X
31. Is the exact middle value of a set of numbers Arrange the numbers in numerical order. Find the value in the middle of the list.
Step 3 of a statistical experiment
The median value
the population cumulants
An experimental study
32. Planning the research - including finding the number of replicates of the study - using the following information: preliminary estimates regarding the size of treatment effects - alternative hypotheses - and the estimated experimental variability. Co
Correlation
the sample or population mean
A probability distribution
Step 1 of a statistical experiment
33. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Statistical dispersion
Marginal distribution
Valid measure
f(z) - and its cdf by F(z).
34. Interpretation of statistical information in that the assumption is that whatever is proposed as a cause has no effect on the variable being measured can often involve the development of a
Null hypothesis
That is the median value
Trend
the sample or population mean
35. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A probability density function
Credence
A sampling distribution
Statistical inference
36. The proportion of the explained variation by a linear regression model in the total variation.
the population cumulants
Coefficient of determination
Quantitative variable
Individual
37. Rejecting a true null hypothesis.
A likelihood function
Type I errors & Type II errors
covariance of X and Y
Type 1 Error
38. Where the null hypothesis is falsely rejected giving a 'false positive'.
Nominal measurements
the population correlation
Type 2 Error
Type I errors
39. (or just likelihood) is a conditional probability function considered a function of its second argument with its first argument held fixed. For example - imagine pulling a numbered ball with the number k from a bag of n balls - numbered 1 to n. Then
Conditional probability
A likelihood function
A random variable
Binomial experiment
40. Describes a characteristic of an individual to be measured or observed.
Variable
Kurtosis
Joint distribution
Null hypothesis
41. Is used to describe probability in a continuous probability distribution. For example - you can't say that the probability of a man being six feet tall is 20% - but you can say he has 20% of chances of being between five and six feet tall. Probabilit
P-value
the sample or population mean
Probability density
the population mean
42. Two variables such that their effects on the response variable cannot be distinguished from each other.
Inferential statistics
Sampling
The sample space
Confounded variables
43. Given two jointly distributed random variables X and Y - the conditional probability distribution of Y given X (written 'Y | X') is the probability distribution of Y when X is known to be a particular value.
Lurking variable
Conditional distribution
Marginal distribution
Sampling frame
44. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Likert scale
Law of Parsimony
Standard error
Bias
45. (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ('value'). Thus - it represents the average amount one 'expects' to win per bet if bets with identical odds are re
A probability density function
Step 2 of a statistical experiment
The Expected value
Correlation coefficient
46. Have no meaningful rank order among values.
Sampling Distribution
Nominal measurements
Outlier
The average - or arithmetic mean
47. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
observational study
A random variable
Placebo effect
Probability density
48. Is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case - the researchers would collect o
hypotheses
A random variable
Observational study
Quantitative variable
49. Is the length of the smallest interval which contains all the data.
Statistic
A probability space
The Range
An Elementary event
50. A group of individuals sharing some common features that might affect the treatment.
Block
Trend
A sample
A probability distribution