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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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clep
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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. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
Conditional distribution
An event
inferential statistics
2. 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
Ratio measurements
Inferential statistics
A data point
3. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
A sampling distribution
Particular realizations of a random variable
P-value
A probability distribution
4. Cov[X - Y] :
Independent Selection
covariance of X and Y
Credence
Sampling
5. Are usually written in upper case roman letters: X - Y - etc.
Random variables
An event
A probability density function
hypothesis
6. Where the null hypothesis is falsely rejected giving a 'false positive'.
Sampling frame
Particular realizations of a random variable
Type I errors
quantitative variables
7. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
experimental studies and observational studies.
f(z) - and its cdf by F(z).
Individual
A Statistical parameter
8. 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.
Particular realizations of a random variable
Conditional distribution
Variability
Type I errors
9. 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.
Probability and statistics
Sampling
Seasonal effect
Nominal measurements
10. 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
A sampling distribution
Placebo effect
s-algebras
Observational study
11. Is defined as the expected value of random variable (X -
descriptive statistics
Statistical inference
The Covariance between two random variables X and Y - with expected values E(X) =
Mutual independence
12. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Reliable measure
nominal - ordinal - interval - and ratio
Average and arithmetic mean
Simple random sample
13. 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
Divide the sum by the number of values.
covariance of X and Y
Step 3 of a statistical experiment
Random variables
14. E[X] :
Seasonal effect
expected value of X
Experimental and observational studies
the population variance
15. 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.
Probability and statistics
Variable
Sampling
Law of Large Numbers
16. 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.
A probability distribution
A population or statistical population
The variance of a random variable
Nominal measurements
17. 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.
Type I errors & Type II errors
The standard deviation
Simple random sample
Dependent Selection
18. 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
Block
the population mean
An experimental study
Mutual independence
19. 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.
f(z) - and its cdf by F(z).
Marginal probability
Sampling frame
Type I errors & Type II errors
20. A numerical facsimilie or representation of a real-world phenomenon.
Simulation
Individual
Trend
Sample space
21. 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.
Type 2 Error
A random variable
Lurking variable
Sample space
22. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
The standard deviation
Binary data
A Distribution function
A Probability measure
23. 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
Power of a test
Null hypothesis
A sampling distribution
Confounded variables
24. Is a measure of the 'peakedness' of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations - as opposed to frequent modestly sized deviations.
Joint distribution
Ratio measurements
Kurtosis
the population cumulants
25. 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).
The Covariance between two random variables X and Y - with expected values E(X) =
Step 2 of a statistical experiment
Confounded variables
Joint probability
26. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
Residuals
Sample space
Simple random sample
27. Many statistical methods seek to minimize the mean-squared error - and these are called
methods of least squares
Marginal probability
quantitative variables
Law of Parsimony
28. Is data that can take only two values - usually represented by 0 and 1.
Probability density
Binary data
Type 2 Error
Skewness
29. Is a sample space over which a probability measure has been defined.
Inferential statistics
experimental studies and observational studies.
hypothesis
A probability space
30. 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.
Marginal probability
That value is the median value
A population or statistical population
The Covariance between two random variables X and Y - with expected values E(X) =
31. 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
Law of Large Numbers
A Statistical parameter
An estimate of a parameter
32. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Power of a test
Bias
Reliable measure
A Random vector
33. Any specific experimental condition applied to the subjects
Treatment
Descriptive statistics
Posterior probability
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
34. In number theory - scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns - which may then lead to
Step 3 of a statistical experiment
Count data
Cumulative distribution functions
hypotheses
35. ?r
Count data
the population cumulants
Variability
A sampling distribution
36. 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
The median value
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
inferential statistics
f(z) - and its cdf by F(z).
37. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
hypotheses
Prior probability
applied statistics
Joint distribution
38. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Bias
Lurking variable
Statistic
categorical variables
39. Two variables such that their effects on the response variable cannot be distinguished from each other.
Conditional distribution
Reliable measure
Confounded variables
Joint distribution
40. The proportion of the explained variation by a linear regression model in the total variation.
Inferential statistics
Sampling
Inferential
Coefficient of determination
41. Probability of accepting a false null hypothesis.
Beta value
Estimator
Placebo effect
Valid measure
42. A list of individuals from which the sample is actually selected.
The median value
A Distribution function
Sampling frame
A sample
43. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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44. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Step 2 of a statistical experiment
Prior probability
A probability distribution
Treatment
45. Is that part of a population which is actually observed.
A sample
A Probability measure
The median value
Independent Selection
46. Var[X] :
variance of X
Simpson's Paradox
Step 3 of a statistical experiment
Variability
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.
the population variance
Skewness
Statistical dispersion
Descriptive
48. When you have two or more competing models - choose the simpler of the two models.
covariance of X and Y
Divide the sum by the number of values.
Law of Parsimony
That is the median value
49. 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
A statistic
Conditional distribution
Greek letters
50. 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
Block
Probability and statistics
Marginal probability