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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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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.
Bias
Probability and statistics
expected value of X
Inferential
2. 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.
A likelihood function
Confounded variables
The median value
Sampling Distribution
3. 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.
An experimental study
Descriptive
Marginal distribution
Interval measurements
4. Gives the probability of events in a probability space.
A sampling distribution
Null hypothesis
A Probability measure
Independence or Statistical independence
5. 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.
the population correlation
Valid measure
Statistical inference
Dependent Selection
6. 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.
Seasonal effect
variance of X
Divide the sum by the number of values.
Type 1 Error
7. The collection of all possible outcomes in an experiment.
The sample space
Kurtosis
variance of X
Sample space
8. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Sampling
A sampling distribution
quantitative variables
The sample space
9. Long-term upward or downward movement over time.
Step 1 of a statistical experiment
An estimate of a parameter
Trend
hypotheses
10. 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
Step 1 of a statistical experiment
Independent Selection
Probability density functions
The Expected value
11. Any specific experimental condition applied to the subjects
Inferential statistics
Coefficient of determination
Treatment
Observational study
12. ?
the population correlation
Treatment
The Covariance between two random variables X and Y - with expected values E(X) =
Bias
13. 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).
Reliable measure
Joint probability
Residuals
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
14. Of a group of numbers is the center point of all those number values.
Probability density
An Elementary event
The average - or arithmetic mean
Binary data
15. Is data that can take only two values - usually represented by 0 and 1.
Binary data
A Random vector
Binomial experiment
The average - or arithmetic mean
16. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Cumulative distribution functions
Posterior probability
the population correlation
Lurking variable
17. 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
Dependent Selection
Descriptive statistics
Probability density functions
Probability
18. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
Conditional distribution
Descriptive statistics
Simpson's Paradox
19. There are two major types of causal statistical studies: In both types of studies - the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies
Seasonal effect
experimental studies and observational studies.
Credence
The Covariance between two random variables X and Y - with expected values E(X) =
20. Data are gathered and correlations between predictors and response are investigated.
Probability
observational study
That is the median value
Residuals
21. Is a process of selecting observations to obtain knowledge about a population. There are many methods to choose on which sample to do the observations.
Sampling
methods of least squares
That is the median value
f(z) - and its cdf by F(z).
22. Is a function that gives the probability of all elements in a given space: see List of probability distributions
nominal - ordinal - interval - and ratio
Ratio measurements
Kurtosis
A probability distribution
23. S^2
the population variance
the population mean
A Distribution function
Quantitative variable
24. To find the average - or arithmetic mean - of a set of numbers:
Divide the sum by the number of values.
A data set
A data point
the population variance
25. Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol. 4. Further examining the data set in secondary analyses - to suggest new hypotheses for future study. 5. Documenting and present
Step 3 of a statistical experiment
descriptive statistics
The median value
An event
26. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Statistics
The Covariance between two random variables X and Y - with expected values E(X) =
The standard deviation
applied statistics
27. A variable describes an individual by placing the individual into a category or a group.
Correlation coefficient
Sampling frame
Qualitative variable
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
28. Another name for elementary event.
Atomic event
the sample or population mean
Law of Large Numbers
Probability
29. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Descriptive
Joint distribution
A sampling distribution
the population cumulants
30. A numerical measure that describes an aspect of a population.
Residuals
The standard deviation
Ratio measurements
Parameter
31. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Reliable measure
Dependent Selection
applied statistics
Independence or Statistical independence
32. Var[X] :
Nominal measurements
The Mean of a random variable
Particular realizations of a random variable
variance of X
33. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
the population variance
Interval measurements
Sampling Distribution
Prior probability
34. Is denoted by - pronounced 'x bar'.
The sample space
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Bias
Skewness
35. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
A data set
s-algebras
Outlier
Parameter
36. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
the population correlation
Individual
Sample space
A statistic
37. Describes the spread in the values of the sample statistic when many samples are taken.
Coefficient of determination
Residuals
Independent Selection
Variability
38. Is a measure of its statistical dispersion - indicating how far from the expected value its values typically are. The variance of random variable X is typically designated as - - or simply s2.
P-value
An Elementary event
The variance of a random variable
Probability density functions
39. Probability of rejecting a true null hypothesis.
Simulation
Binary data
Beta value
Alpha value (Level of Significance)
40. 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
The Covariance between two random variables X and Y - with expected values E(X) =
Conditional distribution
hypothesis
41. Some commonly used symbols for population parameters
the population mean
Estimator
Greek letters
A sample
42. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Binomial experiment
An Elementary event
Dependent Selection
The average - or arithmetic mean
43. 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
Observational study
Descriptive
the population mean
Interval measurements
44. Working from a null hypothesis two basic forms of error are recognized:
A sampling distribution
Type I errors & Type II errors
A statistic
Ratio measurements
45. Failing to reject a false null hypothesis.
Independent Selection
Type 2 Error
Binary data
Interval measurements
46. 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
Bias
Atomic event
Experimental and observational studies
Probability and statistics
47. Are simply two different terms for the same thing. Add the given values
Inferential statistics
A probability distribution
categorical variables
Average and arithmetic mean
48. Two variables such that their effects on the response variable cannot be distinguished from each other.
Kurtosis
Divide the sum by the number of values.
The Range
Confounded variables
49. To prove the guiding theory further - these predictions are tested as well - as part of the scientific method. If the inference holds true - then the descriptive statistics of the new data increase the soundness of that
Residuals
hypothesis
The sample space
Block
50. The proportion of the explained variation by a linear regression model in the total variation.
A sample
Coefficient of determination
Qualitative variable
Step 3 of a statistical experiment