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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
Start Test
Study First
Subjects
:
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
.
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. Working from a null hypothesis two basic forms of error are recognized:
Pairwise independence
Type I errors & Type II errors
variance of X
The Expected value
2. A numerical measure that describes an aspect of a sample.
Variability
A data set
Statistic
Credence
3. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Confounded variables
Descriptive
methods of least squares
The Expected value
4. Probability of accepting a false null hypothesis.
Binomial experiment
f(z) - and its cdf by F(z).
Beta value
P-value
5. 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)
Particular realizations of a random variable
the population correlation
Interval measurements
Placebo effect
6. Is its expected value. The mean (or sample mean of a data set is just the average value.
A sample
The Mean of a random variable
Quantitative variable
Variable
7. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
the population variance
Greek letters
The Mean of a random variable
Residuals
8. (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.
Beta value
Type II errors
A probability space
An Elementary event
9. Is defined as the expected value of random variable (X -
The Covariance between two random variables X and Y - with expected values E(X) =
Binomial experiment
observational study
The Mean of a random variable
10. 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}.
Type I errors
A probability space
The sample space
s-algebras
11. Two variables such that their effects on the response variable cannot be distinguished from each other.
descriptive statistics
An event
Confounded variables
Type II errors
12. Statistical methods can be used for summarizing or describing a collection of data; this is called
methods of least squares
the sample or population mean
The median value
descriptive statistics
13. Cov[X - Y] :
Type I errors
Divide the sum by the number of values.
covariance of X and Y
Type 2 Error
14. Describes a characteristic of an individual to be measured or observed.
Variable
An event
Quantitative variable
A sampling distribution
15. Long-term upward or downward movement over time.
Trend
Descriptive
Cumulative distribution functions
Marginal distribution
16. 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.
Statistics
Conditional distribution
A probability density function
Trend
17. Failing to reject a false null hypothesis.
Treatment
Simple random sample
Type 2 Error
That value is the median value
18. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Type I errors & Type II errors
Probability and statistics
Inferential
Placebo effect
19. Is the length of the smallest interval which contains all the data.
Conditional distribution
The Range
Experimental and observational studies
That is the median value
20. 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'
Statistic
Conditional probability
A probability distribution
Inferential
21. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
categorical variables
A Probability measure
applied statistics
22. 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.
descriptive statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
The median value
hypothesis
23. Gives the probability distribution for a continuous random variable.
A probability space
Estimator
A probability density function
Dependent Selection
24. 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
Binary data
Treatment
That value is the median value
25. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Reliable measure
Greek letters
A probability distribution
An Elementary event
26. 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.
The sample space
Dependent Selection
An experimental study
Step 3 of a statistical experiment
27.
Seasonal effect
Sampling frame
Experimental and observational studies
the population mean
28. 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.
Independent Selection
Ratio measurements
Dependent Selection
Independence or Statistical independence
29. Gives the probability of events in a probability space.
Correlation coefficient
A Probability measure
Parameter
Sampling
30. The probability of correctly detecting a false null hypothesis.
Statistical inference
Power of a test
inferential statistics
variance of X
31. 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
Simulation
A probability space
Type I errors
Mutual independence
32. 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.
Conditional probability
hypothesis
Estimator
Statistical inference
33. Is data arising from counting that can take only non-negative integer values.
The sample space
Count data
Dependent Selection
experimental studies and observational studies.
34. 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
Pairwise independence
Ratio measurements
Joint probability
inferential statistics
35. 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
observational study
Inferential statistics
Probability
Probability density functions
36. 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
A Distribution function
the population correlation
Likert scale
Null hypothesis
37. Probability of rejecting a true null hypothesis.
A probability distribution
Greek letters
Mutual independence
Alpha value (Level of Significance)
38. 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
Independent Selection
Inferential statistics
nominal - ordinal - interval - and ratio
Skewness
39. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Type I errors
Sample space
A statistic
A probability density function
40. To find the average - or arithmetic mean - of a set of numbers:
Divide the sum by the number of values.
nominal - ordinal - interval - and ratio
Ordinal measurements
A Statistical parameter
41. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
A Distribution function
The average - or arithmetic mean
Variable
42. Another name for elementary event.
methods of least squares
The standard deviation
Independence or Statistical independence
Atomic event
43. 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.
Posterior probability
expected value of X
Kurtosis
A population or statistical population
44. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Average and arithmetic mean
The Expected value
Particular realizations of a random variable
Statistics
45. A variable describes an individual by placing the individual into a category or a group.
Statistical inference
Variability
Sample space
Qualitative variable
46. Describes the spread in the values of the sample statistic when many samples are taken.
A sampling distribution
Variability
Seasonal effect
Greek letters
47. Some commonly used symbols for sample statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Ordinal measurements
Inferential statistics
Coefficient of determination
48. A common goal for a statistical research project is to investigate causality - and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response.
Parameter
Experimental and observational studies
Kurtosis
Statistic
49. In particular - the pdf of the standard normal distribution is denoted by
f(z) - and its cdf by F(z).
the population cumulants
Descriptive statistics
The sample space
50. 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 average - or arithmetic mean
nominal - ordinal - interval - and ratio
Statistical inference
experimental studies and observational studies.