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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.
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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. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Probability density functions
Particular realizations of a random variable
Statistic
inferential statistics
2. 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
Correlation coefficient
Mutual independence
That is the median value
Power of a test
3. Is a set of entities about which statistical inferences are to be drawn - often based on random sampling. One can also talk about a population of measurements or values.
A population or statistical population
An experimental study
Marginal probability
covariance of X and Y
4. 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
A Statistical parameter
Ordinal measurements
Probability
Variability
5. Var[X] :
variance of X
Lurking variable
Conditional probability
Dependent Selection
6. 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
A data set
Posterior probability
Descriptive statistics
experimental studies and observational studies.
7. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Treatment
Posterior probability
An estimate of a parameter
the population mean
8. Many statistical methods seek to minimize the mean-squared error - and these are called
s-algebras
Cumulative distribution functions
methods of least squares
Confounded variables
9. 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 probability density function
Cumulative distribution functions
A data point
Descriptive
10. Gives the probability distribution for a continuous random variable.
The Expected value
A probability density function
A data set
applied statistics
11. Is the study of the collection - organization - analysis - and interpretation of data. It deals with all aspects of this - including the planning of data collection in terms of the design of surveys and experiments.
Simple random sample
Type II errors
Statistics
Atomic event
12. Gives the probability of events in a probability space.
A Probability measure
observational study
covariance of X and Y
Atomic event
13. A list of individuals from which the sample is actually selected.
Sampling frame
A probability density function
Bias
Parameter - or 'statistical parameter'
14. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
Credence
Law of Parsimony
Probability
15. Is defined as the expected value of random variable (X -
Alpha value (Level of Significance)
Correlation
The Covariance between two random variables X and Y - with expected values E(X) =
Type I errors & Type II errors
16. Uses patterns in the sample data to draw inferences about the population represented - accounting for randomness. These inferences may take the form of: answering yes/no questions about the data (hypothesis testing) - estimating numerical characteris
Inferential statistics
experimental studies and observational studies.
The Range
The variance of a random variable
17. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
A probability space
A Statistical parameter
The Covariance between two random variables X and Y - with expected values E(X) =
Prior probability
18. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Residuals
Statistical adjustment
Probability
Beta value
19. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Likert scale
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Random variables
Ordinal measurements
20. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
A probability space
Sample space
Greek letters
Valid measure
21. 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
Marginal distribution
Statistical dispersion
Qualitative variable
22. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
23. Is denoted by - pronounced 'x bar'.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
A sampling distribution
Reliable measure
The Range
24. 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)
experimental studies and observational studies.
the population mean
Interval measurements
An estimate of a parameter
25. Two variables such that their effects on the response variable cannot be distinguished from each other.
Likert scale
categorical variables
Confounded variables
Statistic
26. 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
Interval measurements
Ratio measurements
Skewness
Parameter
27. A measure that is relevant or appropriate as a representation of that property.
Average and arithmetic mean
Valid measure
Marginal probability
the sample or population mean
28. Can be a population parameter - a distribution parameter - an unobserved parameter (with different shades of meaning). In statistics - this is often a quantity to be estimated.
29. Long-term upward or downward movement over time.
Trend
Likert scale
An event
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
30. Of a group of numbers is the center point of all those number values.
The average - or arithmetic mean
Standard error
Step 1 of a statistical experiment
the population variance
31. Failing to reject a false null hypothesis.
The standard deviation
observational study
Type 2 Error
Simulation
32. When there is an even number of values...
That is the median value
the population variance
A data point
Seasonal effect
33. Is data that can take only two values - usually represented by 0 and 1.
A sampling distribution
Binary data
nominal - ordinal - interval - and ratio
variance of X
34. Is data arising from counting that can take only non-negative integer values.
Count data
Kurtosis
Sample space
Type I errors
35. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Bias
Ratio measurements
Step 3 of a statistical experiment
nominal - ordinal - interval - and ratio
36. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
Simulation
Residuals
A data set
37. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
Type II errors
Sampling Distribution
Lurking variable
Marginal probability
38. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
observational study
A sampling distribution
Skewness
Placebo effect
39. 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
Correlation coefficient
Null hypothesis
Independence or Statistical independence
expected value of X
40. 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
A Probability measure
hypothesis
applied statistics
Residuals
41. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Correlation
Pairwise independence
Probability
Sampling
42. The collection of all possible outcomes in an experiment.
A random variable
Sample space
Correlation
Step 1 of a statistical experiment
43. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Statistic
A population or statistical population
Inferential
Null hypothesis
44. Also called correlation coefficient - is a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify - for example - how shoe size and height are correlated in the population). An example is the P
A population or statistical population
Correlation
Sampling frame
That is the median value
45. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
A likelihood function
quantitative variables
A sample
Binomial experiment
46. Describes a characteristic of an individual to be measured or observed.
Statistical inference
A Statistical parameter
Sampling
Variable
47. 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
That value is the median value
Step 1 of a statistical experiment
Confounded variables
Type I errors
48. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
An experimental study
Random variables
Independence or Statistical independence
Type II errors
49.
Block
the population mean
Independence or Statistical independence
Alpha value (Level of Significance)
50. In particular - the pdf of the standard normal distribution is denoted by
A likelihood function
descriptive statistics
A probability distribution
f(z) - and its cdf by F(z).