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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. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Alpha value (Level of Significance)
Law of Large Numbers
Correlation coefficient
covariance of X and Y
2. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Variable
A data set
Nominal measurements
Joint distribution
3. 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
the sample or population mean
Conditional distribution
A sampling distribution
4. Is the set of possible outcomes of an experiment. For example - the sample space for rolling a six-sided die will be {1 - 2 - 3 - 4 - 5 - 6}.
A data set
The variance of a random variable
Random variables
The sample space
5. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Count data
Placebo effect
Independence or Statistical independence
Credence
6. 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.
Independent Selection
f(z) - and its cdf by F(z).
Step 2 of a statistical experiment
Probability density functions
7. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Independent Selection
Correlation coefficient
A probability distribution
Statistics
8. Cov[X - Y] :
covariance of X and Y
Treatment
Descriptive
The sample space
9. The collection of all possible outcomes in an experiment.
Ratio measurements
Sample space
Step 2 of a statistical experiment
Count data
10. Working from a null hypothesis two basic forms of error are recognized:
Estimator
Prior probability
Beta value
Type I errors & Type II errors
11. 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)
A Statistical parameter
Interval measurements
Dependent Selection
inferential statistics
12. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Type I errors & Type II errors
categorical variables
A population or statistical population
An event
13. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Simple random sample
hypothesis
Sampling Distribution
Atomic event
14. Is inference about a population from a random sample drawn from it or - more generally - about a random process from its observed behavior during a finite period of time.
Independence or Statistical independence
Statistical inference
Marginal distribution
Marginal probability
15. Two events are independent if the outcome of one does not affect that of the other (for example - getting a 1 on one die roll does not affect the probability of getting a 1 on a second roll). Similarly - when we assert that two random variables are i
Correlation coefficient
Independence or Statistical independence
Probability density
Binomial experiment
16. A variable describes an individual by placing the individual into a category or a group.
A sampling distribution
s-algebras
Experimental and observational studies
Qualitative variable
17. (cdfs) are denoted by upper case letters - e.g. F(x).
covariance of X and Y
Nominal measurements
Cumulative distribution functions
Type 1 Error
18. Of a group of numbers is the center point of all those number values.
Step 1 of a statistical experiment
Trend
The average - or arithmetic mean
Standard error
19. Is the length of the smallest interval which contains all the data.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
experimental studies and observational studies.
The Range
A population or statistical population
20. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Ordinal measurements
Quantitative variable
Law of Parsimony
variance of X
21. 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.
Outlier
A Probability measure
Marginal probability
applied statistics
22. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Dependent Selection
Parameter
A Statistical parameter
A statistic
23. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
Nominal measurements
Mutual independence
Binary data
24. (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
experimental studies and observational studies.
methods of least squares
Bias
25. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
A Random vector
Alpha value (Level of Significance)
P-value
Divide the sum by the number of values.
26. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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27. Where the null hypothesis is falsely rejected giving a 'false positive'.
the population mean
Type I errors
Sample space
Marginal probability
28. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
the sample or population mean
An estimate of a parameter
the population mean
Type 2 Error
29. The standard deviation of a sampling distribution.
The Expected value
Standard error
An experimental study
applied statistics
30. Is its expected value. The mean (or sample mean of a data set is just the average value.
Law of Large Numbers
observational study
P-value
The Mean of a random variable
31. 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
Trend
Observational study
Interval measurements
Inferential
32. Some commonly used symbols for population parameters
the population mean
hypotheses
Individual
inferential statistics
33. Are simply two different terms for the same thing. Add the given values
Binary data
Alpha value (Level of Significance)
Average and arithmetic mean
A sample
34. Is a sample space over which a probability measure has been defined.
Credence
A probability space
Marginal probability
Independence or Statistical independence
35. 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
hypothesis
Parameter
s-algebras
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
36. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Probability density functions
Valid measure
Marginal distribution
Statistical adjustment
37. 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
Atomic event
applied statistics
Probability
That is the median value
38. 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
Dependent Selection
That is the median value
Correlation
Marginal probability
39. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Random variables
Law of Large Numbers
Likert scale
Statistical inference
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.
Experimental and observational studies
the population variance
Sampling
expected value of X
41.
Quantitative variable
the population mean
Individual
s-algebras
42. E[X] :
The Covariance between two random variables X and Y - with expected values E(X) =
The Expected value
Bias
expected value of X
43. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Nominal measurements
Particular realizations of a random variable
applied statistics
the population cumulants
44. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
quantitative variables
Posterior probability
The Mean of a random variable
descriptive statistics
45. Is that part of a population which is actually observed.
A Distribution function
A sample
The standard deviation
Bias
46. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
The Mean of a random variable
Random variables
Binomial experiment
Ratio measurements
47. A numerical measure that assesses the strength of a linear relationship between two variables.
An event
Inferential statistics
Correlation coefficient
An Elementary event
48. 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.
Joint distribution
Sampling
Posterior probability
Independent Selection
49. 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.
s-algebras
A likelihood function
Conditional distribution
A population or statistical population
50. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
nominal - ordinal - interval - and ratio
Joint distribution
Probability
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
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