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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. 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).
Type 1 Error
Joint probability
Experimental and observational studies
applied statistics
2. A measure that is relevant or appropriate as a representation of that property.
Valid measure
Parameter
Inferential
the population mean
3. 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
A data point
Statistical inference
Trend
4. 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
Step 2 of a statistical experiment
Sampling frame
Credence
Correlation
5. Statistical methods can be used for summarizing or describing a collection of data; this is called
Probability and statistics
descriptive statistics
A population or statistical population
Step 3 of a statistical experiment
6. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
The median value
Type I errors & Type II errors
Seasonal effect
Pairwise independence
7. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Binary data
Particular realizations of a random variable
inferential statistics
A random variable
8. A numerical measure that assesses the strength of a linear relationship between two variables.
Kurtosis
categorical variables
The Expected value
Correlation coefficient
9. Many statistical methods seek to minimize the mean-squared error - and these are called
the population correlation
Correlation
Parameter
methods of least squares
10. Working from a null hypothesis two basic forms of error are recognized:
A likelihood function
A population or statistical population
An experimental study
Type I errors & Type II errors
11. 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
hypotheses
Individual
the population variance
Inferential statistics
12. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Sampling Distribution
Interval measurements
the sample or population mean
Ordinal measurements
13. Cov[X - Y] :
Average and arithmetic mean
covariance of X and Y
Dependent Selection
Law of Large Numbers
14. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Likert scale
Statistical adjustment
A Random vector
Coefficient of determination
15. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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16. 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
Parameter
Marginal distribution
Power of a test
Step 1 of a statistical experiment
17. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
A random variable
Joint distribution
Placebo effect
Credence
18. 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
Type I errors
Lurking variable
Step 2 of a statistical experiment
Inferential
19. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Lurking variable
A probability distribution
Probability density
Independent Selection
20. 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
Seasonal effect
The Expected value
An estimate of a parameter
Ratio measurements
21. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Type 1 Error
Correlation
Sampling Distribution
The variance of a random variable
22. Probability of accepting a false null hypothesis.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Seasonal effect
Beta value
Binary data
23. Are usually written in upper case roman letters: X - Y - etc.
Random variables
Nominal measurements
Statistical adjustment
The Expected value
24. The standard deviation of a sampling distribution.
Variability
That is the median value
Coefficient of determination
Standard error
25. Describes a characteristic of an individual to be measured or observed.
Binary data
Variable
Independent Selection
The average - or arithmetic mean
26. Is a measure of the asymmetry of the probability distribution of a real-valued random variable. Roughly speaking - a distribution has positive skew (right-skewed) if the higher tail is longer and negative skew (left-skewed) if the lower tail is longe
Lurking variable
Quantitative variable
Skewness
Individual
27. A numerical measure that describes an aspect of a sample.
Inferential
An estimate of a parameter
Statistic
Cumulative distribution functions
28. Is a sample and the associated data points.
Null hypothesis
Correlation
Skewness
A data set
29. Two variables such that their effects on the response variable cannot be distinguished from each other.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
observational study
Confounded variables
Residuals
30. Some commonly used symbols for population parameters
Pairwise independence
the population mean
An event
methods of least squares
31. Samples are drawn from two different populations such that the sample data drawn from one population is completely unrelated to the selection of sample data from the other population.
Reliable measure
That is the median value
Independent Selection
A statistic
32. 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
experimental studies and observational studies.
The sample space
A Statistical parameter
Statistics
33. To find the average - or arithmetic mean - of a set of numbers:
Divide the sum by the number of values.
Posterior probability
A population or statistical population
Probability density
34. In particular - the pdf of the standard normal distribution is denoted by
Particular realizations of a random variable
Binary data
f(z) - and its cdf by F(z).
The average - or arithmetic mean
35. Can refer either to a sample not being representative of the population - or to the difference between the expected value of an estimator and the true value.
Beta value
A Random vector
Joint distribution
Bias
36. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Probability and statistics
Interval measurements
Likert scale
Block
37. A group of individuals sharing some common features that might affect the treatment.
Beta value
The Expected value
Block
Ordinal measurements
38. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Binomial experiment
Probability and statistics
A Probability measure
Sample space
39. 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.
The variance of a random variable
Probability and statistics
The standard deviation
Inferential
40. A common goal for a statistical research project is to investigate causality - and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response.
Probability and statistics
Statistical dispersion
Experimental and observational studies
Power of a test
41. Is the probability of some event A - assuming event B. Conditional probability is written P(A|B) - and is read 'the probability of A - given B'
A probability distribution
Conditional probability
nominal - ordinal - interval - and ratio
Likert scale
42. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Count data
Inferential statistics
Prior probability
Cumulative distribution functions
43. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
A statistic
Average and arithmetic mean
Correlation coefficient
Coefficient of determination
44. Any specific experimental condition applied to the subjects
A random variable
descriptive statistics
Step 3 of a statistical experiment
Treatment
45. Probability of rejecting a true null hypothesis.
methods of least squares
Alpha value (Level of Significance)
the population correlation
Ordinal measurements
46. 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.
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47. Involves taking measurements of the system under study - manipulating the system - and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.
observational study
An experimental study
Bias
Observational study
48. A numerical measure that describes an aspect of a population.
Cumulative distribution functions
descriptive statistics
Variable
Parameter
49. (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
Binary data
Pairwise independence
A likelihood function
Probability density functions
50. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Binary data
Confounded variables
Inferential
Descriptive