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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. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Descriptive
expected value of X
nominal - ordinal - interval - and ratio
Cumulative distribution functions
2. Is a sample space over which a probability measure has been defined.
Sampling Distribution
observational study
The Range
A probability space
3. 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)
Random variables
Interval measurements
A Distribution function
s-algebras
4. 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
Skewness
A Distribution function
nominal - ordinal - interval - and ratio
Inferential statistics
5. A group of individuals sharing some common features that might affect the treatment.
covariance of X and Y
methods of least squares
Block
A data set
6. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Inferential statistics
Marginal probability
categorical variables
Type II errors
7. Some commonly used symbols for sample statistics
That value is the median value
An experimental study
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Coefficient of determination
8. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
An Elementary event
Probability density functions
Prior probability
An experimental study
9. 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
hypotheses
the population correlation
nominal - ordinal - interval - and ratio
Particular realizations of a random variable
10. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Marginal distribution
Ordinal measurements
Conditional probability
Inferential
11. Probability of rejecting a true null hypothesis.
Alpha value (Level of Significance)
Null hypothesis
applied statistics
Residuals
12. 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.
Kurtosis
Alpha value (Level of Significance)
Type 1 Error
Divide the sum by the number of values.
13. 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
Cumulative distribution functions
Observational study
A population or statistical population
the population cumulants
14. 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
expected value of X
A probability density function
Dependent Selection
Step 2 of a statistical experiment
15. Is used to describe probability in a continuous probability distribution. For example - you can't say that the probability of a man being six feet tall is 20% - but you can say he has 20% of chances of being between five and six feet tall. Probabilit
Probability density
Type 2 Error
Outlier
A probability space
16. A subjective estimate of probability.
Reliable measure
Credence
Joint distribution
Sample space
17. A data value that falls outside the overall pattern of the graph.
The Mean of a random variable
covariance of X and Y
Outlier
s-algebras
18. 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.
Conditional distribution
Seasonal effect
Variable
Coefficient of determination
19. Is data that can take only two values - usually represented by 0 and 1.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Marginal distribution
Parameter - or 'statistical parameter'
Binary data
20. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
A probability distribution
Descriptive
Observational study
s-algebras
21. Cov[X - Y] :
Statistic
Null hypothesis
Descriptive statistics
covariance of X and Y
22. A numerical facsimilie or representation of a real-world phenomenon.
Simulation
Bias
Beta value
Statistical dispersion
23. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Divide the sum by the number of values.
Individual
Cumulative distribution functions
Sample space
24. Have no meaningful rank order among values.
Likert scale
Skewness
Nominal measurements
expected value of X
25. Are two related but separate academic disciplines. Statistical analysis often uses probability distributions - and the two topics are often studied together. However - probability theory contains much that is of mostly of mathematical interest and no
Probability and statistics
Sampling Distribution
Statistic
Statistics
26. Is data arising from counting that can take only non-negative integer values.
Variable
A sample
Count data
expected value of X
27.
Placebo effect
the population mean
The Range
the population variance
28. 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 Expected value
A sample
Statistical dispersion
Statistical inference
29. Is that part of a population which is actually observed.
Sampling
A sample
Observational study
Null hypothesis
30. 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
Mutual independence
Binomial experiment
Block
31. Data are gathered and correlations between predictors and response are investigated.
observational study
Probability density
Sampling Distribution
Statistic
32. 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.
Step 1 of a statistical experiment
experimental studies and observational studies.
An experimental study
observational study
33. Is a parameter that indexes a family of probability distributions.
Count data
Estimator
A Statistical parameter
Binomial experiment
34. 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'
Conditional probability
Joint distribution
hypothesis
the population mean
35. (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ('value'). Thus - it represents the average amount one 'expects' to win per bet if bets with identical odds are re
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
The Expected value
Type 1 Error
Valid measure
36. Working from a null hypothesis two basic forms of error are recognized:
Alpha value (Level of Significance)
Type I errors & Type II errors
Experimental and observational studies
the population variance
37. 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.
Interval measurements
Random variables
That value is the median value
the population mean
38. A numerical measure that assesses the strength of a linear relationship between two variables.
The standard deviation
Residuals
inferential statistics
Correlation coefficient
39. S^2
the population variance
Atomic event
Random variables
Sampling Distribution
40. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
variance of X
Statistics
Sampling Distribution
The Expected value
41. Is its expected value. The mean (or sample mean of a data set is just the average value.
Estimator
Posterior probability
Nominal measurements
The Mean of a random variable
42. The collection of all possible outcomes in an experiment.
Sample space
Prior probability
Alpha value (Level of Significance)
Variability
43. 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
Probability and statistics
Atomic event
Independence or Statistical independence
44. Are usually written in upper case roman letters: X - Y - etc.
Null hypothesis
Random variables
Skewness
Descriptive statistics
45. 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.
Block
Binomial experiment
A random variable
covariance of X and Y
46. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Independence or Statistical independence
A population or statistical population
expected value of X
Law of Large Numbers
47. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Average and arithmetic mean
Statistic
Placebo effect
categorical variables
48. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
A sample
Inferential
Probability
49. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
Bias
An estimate of a parameter
Likert scale
50. In particular - the pdf of the standard normal distribution is denoted by
Independence or Statistical independence
An event
Average and arithmetic mean
f(z) - and its cdf by F(z).