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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.
Placebo effect
the population correlation
The median value
An event
2. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Placebo effect
Reliable measure
methods of least squares
Confounded variables
3. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
observational study
The Range
Joint distribution
Marginal distribution
4. 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
Count data
Observational study
Type II errors
Marginal distribution
5. 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
Particular realizations of a random variable
Statistics
experimental studies and observational studies.
Bias
6. 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)
nominal - ordinal - interval - and ratio
Marginal distribution
Interval measurements
Particular realizations of a random variable
7. A list of individuals from which the sample is actually selected.
The standard deviation
Experimental and observational studies
Sampling frame
Bias
8. The probability of correctly detecting a false null hypothesis.
f(z) - and its cdf by F(z).
Divide the sum by the number of values.
Power of a test
Beta value
9. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Experimental and observational studies
The variance of a random variable
Inferential
Correlation coefficient
10. 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.
Particular realizations of a random variable
Seasonal effect
That is the median value
A random variable
11. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Binomial experiment
hypothesis
Interval measurements
categorical variables
12. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
A statistic
Simpson's Paradox
Conditional distribution
13. ?
the population correlation
The standard deviation
Joint probability
hypotheses
14. (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 population or statistical population
Individual
A likelihood function
Power of a test
15. 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.
Power of a test
Estimator
A sampling distribution
An estimate of a parameter
16. Many statistical methods seek to minimize the mean-squared error - and these are called
The sample space
methods of least squares
An experimental study
Variable
17. Given two jointly distributed random variables X and Y - the conditional probability distribution of Y given X (written 'Y | X') is the probability distribution of Y when X is known to be a particular value.
Sampling Distribution
Outlier
Conditional distribution
Estimator
18. 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.
Statistical adjustment
Coefficient of determination
Joint probability
Dependent Selection
19. 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}.
Interval measurements
The sample space
Variability
categorical variables
20. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Variable
Interval measurements
Bias
Residuals
21. Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol. 4. Further examining the data set in secondary analyses - to suggest new hypotheses for future study. 5. Documenting and present
Law of Large Numbers
the sample or population mean
Step 3 of a statistical experiment
A Statistical parameter
22. Is a subset of the sample space - to which a probability can be assigned. For example - on rolling a die - 'getting a five or a six' is an event (with a probability of one third if the die is fair).
Simulation
Step 2 of a statistical experiment
inferential statistics
An event
23. Probability of accepting a false null hypothesis.
Conditional distribution
Beta value
Treatment
Probability density
24. Summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types (like heights or weights) - while frequency and percentage are
Step 1 of a statistical experiment
Descriptive statistics
Binomial experiment
A sample
25. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
applied statistics
Count data
A Probability measure
s-algebras
26. 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
Divide the sum by the number of values.
Probability
Type 1 Error
Correlation coefficient
27. 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
A probability distribution
Sample space
Ordinal measurements
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
Statistical inference
Joint probability
hypothesis
29. A measure that is relevant or appropriate as a representation of that property.
Valid measure
Joint probability
An estimate of a parameter
The Range
30. Is its expected value. The mean (or sample mean of a data set is just the average value.
Marginal distribution
Simple random sample
Placebo effect
The Mean of a random variable
31. Var[X] :
Binary data
Trend
variance of X
Divide the sum by the number of values.
32. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
That value is the median value
Binomial experiment
Trend
Type II errors
33. Gives the probability of events in a probability space.
hypothesis
A Probability measure
f(z) - and its cdf by F(z).
Outlier
34. E[X] :
Lurking variable
expected value of X
Reliable measure
The Range
35. 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'
Probability density
Conditional probability
Correlation
Alpha value (Level of Significance)
36. A numerical measure that assesses the strength of a linear relationship between two variables.
The average - or arithmetic mean
methods of least squares
Correlation coefficient
Outlier
37. Any specific experimental condition applied to the subjects
Parameter - or 'statistical parameter'
Independent Selection
Alpha value (Level of Significance)
Treatment
38. When there is an even number of values...
Bias
The sample space
s-algebras
That is the median value
39. 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
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Correlation coefficient
Type 2 Error
Mutual independence
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
Outlier
A population or statistical population
hypothesis
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
41. 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.
Qualitative variable
Descriptive statistics
That value is the median value
Binary data
42. 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
Beta value
Treatment
Experimental and observational studies
Step 1 of a statistical experiment
43. ?r
Step 2 of a statistical experiment
the population cumulants
Statistical inference
Sample space
44. Is the length of the smallest interval which contains all the data.
The Range
Bias
inferential statistics
applied statistics
45. 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.
Marginal probability
Atomic event
That value is the median value
Observational study
46. 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
Type II errors
The sample space
Null hypothesis
categorical variables
47. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Lurking variable
Trend
Statistical dispersion
Interval measurements
48. In particular - the pdf of the standard normal distribution is denoted by
f(z) - and its cdf by F(z).
Count data
A Statistical parameter
Law of Large Numbers
49. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Marginal distribution
Type I errors & Type II errors
A Random vector
Null hypothesis
50. 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
Simulation
Independent Selection
Independence or Statistical independence
Lurking variable