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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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Subjects
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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 exact middle value of a set of numbers Arrange the numbers in numerical order. Find the value in the middle of the list.
An experimental study
Greek letters
A probability density function
The median value
2. The proportion of the explained variation by a linear regression model in the total variation.
The Range
observational study
Coefficient of determination
expected value of X
3. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
experimental studies and observational studies.
Pairwise independence
Statistical dispersion
That value is the median value
4. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
A sampling distribution
Mutual independence
Atomic event
5. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Independent Selection
Bias
Inferential
Law of Parsimony
6. Gives the probability distribution for a continuous random variable.
Sampling frame
Probability
The Expected value
A probability density function
7. Cov[X - Y] :
covariance of X and Y
Estimator
Random variables
A Random vector
8. A numerical measure that describes an aspect of a population.
Divide the sum by the number of values.
Statistical adjustment
Parameter
Placebo effect
9. Patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations - and are then used for drawing inferences about the process or population being studied; this is called
inferential statistics
A sampling distribution
Kurtosis
Statistics
10. Where the null hypothesis is falsely rejected giving a 'false positive'.
Type I errors
hypotheses
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
the population mean
11. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Particular realizations of a random variable
Interval measurements
Ordinal measurements
Nominal measurements
12. A numerical facsimilie or representation of a real-world phenomenon.
Simulation
Trend
experimental studies and observational studies.
Particular realizations of a random variable
13. 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
Beta value
A population or statistical population
A data point
14. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Variability
Credence
Law of Large Numbers
Beta value
15. Describes the spread in the values of the sample statistic when many samples are taken.
Variability
f(z) - and its cdf by F(z).
experimental studies and observational studies.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
16. Rejecting a true null hypothesis.
Divide the sum by the number of values.
the population mean
Type 1 Error
Type 2 Error
17. A numerical measure that assesses the strength of a linear relationship between two variables.
Parameter
Correlation coefficient
An estimate of a parameter
Type 2 Error
18. Working from a null hypothesis two basic forms of error are recognized:
A probability density function
Type I errors & Type II errors
Type I errors
Posterior probability
19. Can be - for example - the possible outcomes of a dice roll (but it is not assigned a value). The distribution function of a random variable gives the probability of different results. We can also derive the mean and variance of a random variable.
A random variable
the population correlation
Standard error
the sample or population mean
20. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Joint distribution
Bias
Average and arithmetic mean
Qualitative variable
21. 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.
Cumulative distribution functions
An experimental study
Joint distribution
That is the median value
22. Is data that can take only two values - usually represented by 0 and 1.
the population mean
Variability
Binary data
Bias
23. 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.
Marginal distribution
Independence or Statistical independence
s-algebras
Probability
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)
Interval measurements
quantitative variables
Type 2 Error
Sample space
25. Is defined as the expected value of random variable (X -
The Covariance between two random variables X and Y - with expected values E(X) =
Beta value
variance of X
Probability
26. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
Confounded variables
Random variables
Beta value
27. 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.
Step 1 of a statistical experiment
A population or statistical population
Variability
Bias
28. 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).
Conditional distribution
Joint probability
Posterior probability
Marginal distribution
29. Are simply two different terms for the same thing. Add the given values
An estimate of a parameter
Nominal measurements
Average and arithmetic mean
Inferential
30. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
A statistic
Type II errors
Placebo effect
A data point
31. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Conditional distribution
That is the median value
Descriptive
A Statistical parameter
32. 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
Credence
An estimate of a parameter
A Statistical parameter
33. 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.
Average and arithmetic mean
Alpha value (Level of Significance)
Independent Selection
observational study
34. The collection of all possible outcomes in an experiment.
Sample space
Observational study
the population mean
A population or statistical population
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
A probability distribution
Skewness
The median value
A likelihood function
36. ?
the population correlation
A Random vector
Conditional distribution
f(z) - and its cdf by F(z).
37. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
hypothesis
Pairwise independence
The variance of a random variable
The average - or arithmetic mean
38. 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.
Qualitative variable
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
The sample space
Bias
39. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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40. 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}.
The sample space
The average - or arithmetic mean
Inferential statistics
applied statistics
41. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
the population mean
Residuals
Pairwise independence
The sample space
42. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Type I errors & Type II errors
Likert scale
Correlation
Statistics
43. 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
A sampling distribution
Coefficient of determination
Type I errors
Inferential statistics
44. A data value that falls outside the overall pattern of the graph.
The standard deviation
Particular realizations of a random variable
Outlier
observational study
45. To find the median value of a set of numbers: Arrange the numbers in numerical order. Locate the two middle numbers in the list. Find the average of those two middle values.
That value is the median value
Law of Large Numbers
Probability density functions
A data point
46. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
the population mean
A probability distribution
Placebo effect
An estimate of a parameter
47. Data are gathered and correlations between predictors and response are investigated.
Step 3 of a statistical experiment
observational study
A sampling distribution
Simulation
48. 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 arithmetic mean of a set of numbers x1 - x2 - ... - xn
Probability
Law of Parsimony
Particular realizations of a random variable
49. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
nominal - ordinal - interval - and ratio
The Covariance between two random variables X and Y - with expected values E(X) =
Sampling Distribution
Type I errors
50. Statistical methods can be used for summarizing or describing a collection of data; this is called
An estimate of a parameter
A statistic
Particular realizations of a random variable
descriptive statistics