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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. 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
Conditional probability
Nominal measurements
Inferential statistics
2. (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
Nominal measurements
Inferential statistics
A likelihood function
A sampling distribution
3. A group of individuals sharing some common features that might affect the treatment.
Kurtosis
Block
Statistic
Probability
4. Is data that can take only two values - usually represented by 0 and 1.
Correlation coefficient
Binary data
Simulation
The Covariance between two random variables X and Y - with expected values E(X) =
5. Two variables such that their effects on the response variable cannot be distinguished from each other.
A data point
Joint probability
Seasonal effect
Confounded variables
6. Is a measure of its statistical dispersion - indicating how far from the expected value its values typically are. The variance of random variable X is typically designated as - - or simply s2.
A sample
Block
The variance of a random variable
A data point
7. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Greek letters
Inferential statistics
Credence
A data set
8. 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 population mean
Residuals
the sample or population mean
9. 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.
Posterior probability
A population or statistical population
The Mean of a random variable
the population variance
10. 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).
Joint probability
Posterior probability
Estimator
Qualitative variable
11. To find the average - or arithmetic mean - of a set of numbers:
Correlation
categorical variables
Average and arithmetic mean
Divide the sum by the number of values.
12. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
Estimator
Independent Selection
Sampling Distribution
13. Probability of accepting a false null hypothesis.
Beta value
An estimate of a parameter
Statistic
Nominal measurements
14. Probability of rejecting a true null hypothesis.
Probability
Greek letters
Alpha value (Level of Significance)
That value is the median value
15. The probability of correctly detecting a false null hypothesis.
Joint probability
P-value
Power of a test
nominal - ordinal - interval - and ratio
16. 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)
A population or statistical population
Individual
Random variables
Interval measurements
17. Is the length of the smallest interval which contains all the data.
The Range
Kurtosis
Type I errors
Treatment
18. (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 sample space
Statistical dispersion
Sampling Distribution
Type I errors
19. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Coefficient of determination
Residuals
Parameter
Standard error
20. 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.
Sampling Distribution
Statistic
That value is the median value
Estimator
21. Is denoted by - pronounced 'x bar'.
The variance of a random variable
A sampling distribution
Placebo effect
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
22. Of a group of numbers is the center point of all those number values.
descriptive statistics
The average - or arithmetic mean
Experimental and observational studies
Joint probability
23. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A sampling distribution
Valid measure
An estimate of a parameter
covariance of X and Y
24. E[X] :
Sampling frame
expected value of X
Law of Large Numbers
Simpson's Paradox
25. 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
Parameter
Step 1 of a statistical experiment
Statistic
A sample
26. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Statistical inference
Atomic event
Inferential
Bias
27. 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.
A likelihood function
Statistical inference
The standard deviation
Marginal distribution
28. 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.
the population mean
Random variables
The average - or arithmetic mean
Marginal distribution
29. 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
Posterior probability
Step 3 of a statistical experiment
Divide the sum by the number of values.
The sample space
30. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Individual
descriptive statistics
the sample or population mean
Null hypothesis
31. (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
Observational study
the population cumulants
A sample
32. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
A Distribution function
Statistical adjustment
Ratio measurements
descriptive statistics
33. A numerical facsimilie or representation of a real-world phenomenon.
Null hypothesis
Simulation
the population correlation
Descriptive
34. Have no meaningful rank order among values.
Inferential
Nominal measurements
An experimental study
Sampling Distribution
35. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Treatment
f(z) - and its cdf by F(z).
categorical variables
Parameter
36. ?
the population correlation
Credence
Sampling Distribution
Coefficient of determination
37. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Mutual independence
Probability density functions
Sample space
Count data
38. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
A probability space
Pairwise independence
Posterior probability
The Covariance between two random variables X and Y - with expected values E(X) =
39. 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
Inferential statistics
Conditional probability
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Type I errors
40. Some commonly used symbols for sample statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Qualitative variable
The sample space
The Range
41. Where the null hypothesis is falsely rejected giving a 'false positive'.
Type II errors
A probability space
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Type I errors
42. 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
Independence or Statistical independence
Bias
Skewness
Type I errors
43. 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
covariance of X and Y
Joint probability
applied statistics
Observational study
44. Cov[X - Y] :
Seasonal effect
Trend
covariance of X and Y
Probability density functions
45. 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.
variance of X
The median value
Likert scale
An estimate of a parameter
46. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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47. Gives the probability of events in a probability space.
A Probability measure
the population mean
the population cumulants
Beta value
48. A numerical measure that assesses the strength of a linear relationship between two variables.
Standard error
The median value
Residuals
Correlation coefficient
49. 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.
A data point
Type I errors & Type II errors
Sampling frame
Individual
50. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Sample space
A probability distribution
Statistics
The Mean of a random variable