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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. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Quantitative variable
Atomic event
expected value of X
An experimental study
2. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Block
Count data
Skewness
The standard deviation
3. Is defined as the expected value of random variable (X -
Quantitative variable
descriptive statistics
The Covariance between two random variables X and Y - with expected values E(X) =
f(z) - and its cdf by F(z).
4. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
variance of X
s-algebras
A population or statistical population
Inferential
5. A list of individuals from which the sample is actually selected.
Sampling frame
Parameter - or 'statistical parameter'
Sample space
Individual
6. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Dependent Selection
Descriptive
Probability density functions
An experimental study
7. Where the null hypothesis is falsely rejected giving a 'false positive'.
quantitative variables
Residuals
Type I errors
Ratio measurements
8. 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
Type 1 Error
An event
Sampling frame
Observational study
9. (cdfs) are denoted by upper case letters - e.g. F(x).
Variable
Standard error
Probability and statistics
Cumulative distribution functions
10. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Statistical adjustment
Binary data
Pairwise independence
covariance of X and Y
11. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Ordinal measurements
hypotheses
Marginal distribution
A Random vector
12. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Count data
Sample space
Law of Large Numbers
A data set
13. 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)
Type II errors
Interval measurements
That value is the median value
s-algebras
14. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Block
Coefficient of determination
Greek letters
Likert scale
15. When you have two or more competing models - choose the simpler of the two models.
Law of Parsimony
The average - or arithmetic mean
Interval measurements
Alpha value (Level of Significance)
16. Gives the probability distribution for a continuous random variable.
A probability density function
An experimental study
Nominal measurements
The average - or arithmetic mean
17. ?
s-algebras
the population correlation
Lurking variable
The average - or arithmetic mean
18. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
Statistic
observational study
An Elementary event
19. 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 variance of a random variable
Probability
Probability density
An event
20. Is a parameter that indexes a family of probability distributions.
Sampling
f(z) - and its cdf by F(z).
A Statistical parameter
Probability density functions
21. A numerical measure that describes an aspect of a population.
A probability space
Variability
Parameter
A sampling distribution
22. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
inferential statistics
The median value
An estimate of a parameter
A Random vector
23. 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
Type II errors
Posterior probability
Skewness
Probability density
24. Rejecting a true null hypothesis.
Type 1 Error
Lurking variable
P-value
the population correlation
25. (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.
An Elementary event
the population cumulants
applied statistics
observational study
26. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
Average and arithmetic mean
observational study
Seasonal effect
27. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Independent Selection
quantitative variables
Statistical inference
A probability distribution
28. 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
A Probability measure
expected value of X
f(z) - and its cdf by F(z).
Mutual independence
29. Working from a null hypothesis two basic forms of error are recognized:
quantitative variables
Descriptive statistics
Type I errors & Type II errors
covariance of X and Y
30. Is the function that gives the probability distribution of a random variable. It cannot be negative - and its integral on the probability space is equal to 1.
Block
Independent Selection
Divide the sum by the number of values.
A Distribution function
31. 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}.
Step 3 of a statistical experiment
Law of Parsimony
Statistical dispersion
The sample space
32. 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
Prior probability
Inferential statistics
the population correlation
Descriptive statistics
33. Is denoted by - pronounced 'x bar'.
Lurking variable
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Atomic event
observational study
34. Is a sample space over which a probability measure has been defined.
Correlation coefficient
The variance of a random variable
A probability space
The average - or arithmetic mean
35. (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
Experimental and observational studies
A likelihood function
The sample space
Marginal probability
36. 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
the population correlation
Bias
A population or statistical population
37. 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
Binary data
Type 1 Error
methods of least squares
38. Many statistical methods seek to minimize the mean-squared error - and these are called
Statistical adjustment
Correlation coefficient
methods of least squares
That value is the median value
39. 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
Cumulative distribution functions
A sample
inferential statistics
40. E[X] :
Observational study
expected value of X
Block
Reliable measure
41. 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
Variable
Step 2 of a statistical experiment
The average - or arithmetic mean
Simple random sample
42. 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.
Lurking variable
s-algebras
Correlation coefficient
Estimator
43. A group of individuals sharing some common features that might affect the treatment.
Block
Interval measurements
Treatment
Descriptive
44. To find the average - or arithmetic mean - of a set of numbers:
Null hypothesis
nominal - ordinal - interval - and ratio
Standard error
Divide the sum by the number of values.
45. 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.
categorical variables
Qualitative variable
applied statistics
A data point
46. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Type I errors & Type II errors
Pairwise independence
Estimator
Descriptive statistics
47. 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.
The variance of a random variable
Individual
Prior probability
Statistical inference
48. 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.
Pairwise independence
Seasonal effect
Standard error
Inferential
49. 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
Independent Selection
Alpha value (Level of Significance)
Valid measure
Correlation
50. ?r
the population cumulants
f(z) - and its cdf by F(z).
A probability space
Trend