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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. Is defined as the expected value of random variable (X -
The Covariance between two random variables X and Y - with expected values E(X) =
A population or statistical population
Joint distribution
Interval measurements
2. 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.
observational study
Binomial experiment
Marginal distribution
The Range
3. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Standard error
the sample or population mean
The variance of a random variable
Confounded variables
4. A numerical measure that assesses the strength of a linear relationship between two variables.
Marginal probability
Correlation coefficient
A population or statistical population
Type II errors
5. 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).
Inferential
Joint probability
Statistics
covariance of X and Y
6. Is a function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. The mean can be used as an estimator.
A data point
A sample
An estimate of a parameter
Estimator
7. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Average and arithmetic mean
quantitative variables
Coefficient of determination
Quantitative variable
8. 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.
Alpha value (Level of Significance)
Seasonal effect
Marginal probability
quantitative variables
9. Design of experiments - using blocking to reduce the influence of confounding variables - and randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error. At this stage - the experimenters a
The sample space
Step 2 of a statistical experiment
Confounded variables
Qualitative variable
10. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Joint distribution
Probability density functions
quantitative variables
Standard error
11. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
An event
Step 2 of a statistical experiment
descriptive statistics
applied statistics
12. 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.
The median value
Bias
A probability distribution
A random variable
13. A numerical measure that describes an aspect of a population.
the population correlation
Bias
expected value of X
Parameter
14. E[X] :
A probability space
Statistic
expected value of X
Prior probability
15. Is data arising from counting that can take only non-negative integer values.
Sampling Distribution
Average and arithmetic mean
Count data
nominal - ordinal - interval - and ratio
16. Gives the probability distribution for a continuous random variable.
Type I errors & Type II errors
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Type 2 Error
A probability density function
17. Two variables such that their effects on the response variable cannot be distinguished from each other.
Observational study
Confounded variables
The Covariance between two random variables X and Y - with expected values E(X) =
Conditional probability
18. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
Marginal probability
Step 3 of a statistical experiment
Null hypothesis
19. Probability of rejecting a true null hypothesis.
descriptive statistics
Statistical dispersion
Alpha value (Level of Significance)
Bias
20. (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
Ratio measurements
covariance of X and Y
Type I errors & Type II errors
21. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Skewness
Type I errors & Type II errors
Bias
A data point
22. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
Lurking variable
descriptive statistics
The standard deviation
23. Var[X] :
variance of X
Standard error
Inferential statistics
Type II errors
24. (or atomic event) is an event with only one element. For example - when pulling a card out of a deck - 'getting the jack of spades' is an elementary event - while 'getting a king or an ace' is not.
the population mean
Descriptive statistics
An Elementary event
Descriptive
25. Failing to reject a false null hypothesis.
Pairwise independence
Skewness
Type 2 Error
Step 3 of a statistical experiment
26. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
The average - or arithmetic mean
Atomic event
A probability space
Pairwise independence
27. 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
Power of a test
Step 1 of a statistical experiment
Pairwise independence
Descriptive statistics
28. Is denoted by - pronounced 'x bar'.
categorical variables
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Trend
Ratio measurements
29. 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
The average - or arithmetic mean
Type 2 Error
descriptive statistics
Probability density
30. When you have two or more competing models - choose the simpler of the two models.
A population or statistical population
the population mean
Law of Parsimony
Statistical inference
31. A sample selected in such a way that each individual is equally likely to be selected as well as any group of size n is equally likely to be selected.
Simple random sample
Type II errors
Prior probability
f(z) - and its cdf by F(z).
32. Where the null hypothesis is falsely rejected giving a 'false positive'.
Nominal measurements
Type I errors
Valid measure
A statistic
33. A data value that falls outside the overall pattern of the graph.
Conditional distribution
The variance of a random variable
Outlier
Coefficient of determination
34. Are simply two different terms for the same thing. Add the given values
f(z) - and its cdf by F(z).
Power of a test
Nominal measurements
Average and arithmetic mean
35. A measurement such that the random error is small
the population mean
Reliable measure
Bias
the population correlation
36. Any specific experimental condition applied to the subjects
Treatment
Probability
Probability and statistics
Kurtosis
37. Is a sample space over which a probability measure has been defined.
Variability
A probability space
observational study
Individual
38. The probability of correctly detecting a false null hypothesis.
A data set
Estimator
the population mean
Power of a test
39. Some commonly used symbols for population parameters
Alpha value (Level of Significance)
Probability density
A Statistical parameter
the population mean
40. 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
Law of Parsimony
Power of a test
Observational study
Cumulative distribution functions
41. 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
Marginal probability
Observational study
Step 1 of a statistical experiment
variance of X
42. 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
The average - or arithmetic mean
The Mean of a random variable
Probability
Type I errors & Type II errors
43. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
observational study
Greek letters
Probability and statistics
Sampling frame
44. Have meaningful distances between measurements defined - but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit)
Interval measurements
variance of X
Independence or Statistical independence
hypotheses
45. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Step 2 of a statistical experiment
the population mean
A population or statistical population
Posterior probability
46. Have imprecise differences between consecutive values - but have a meaningful order to those values
variance of X
Ordinal measurements
A Distribution function
Cumulative distribution functions
47. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
Ordinal measurements
Probability and statistics
Confounded variables
48. 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
Trend
hypotheses
Law of Parsimony
Mutual independence
49. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
quantitative variables
Estimator
Bias
Reliable measure
50. Cov[X - Y] :
Statistic
A Probability measure
covariance of X and Y
applied statistics