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Terms in this set (65)
Measures of Centrality
Mean
Median
Mode
Mean
- Sum of all the values in the population/sample
divided by the number of values
Median
Middle value in a set of ordered data (key word: ordered)
Mode
Number/value that occurs most frequently (can be bi-modal or have no mode)
Measures of Dispersion
Variance
Standard Deviation
Range
Variance
Average squared distance from the mean
Standard Deviation
Positive square root of the variance
Range
Highest # minus the lowest #
Sample
A portion, or part, of the population of interest
Population
The entire set of individuals/objects of interest.
Statistic
A characteristic of a sample
Parameter
A characteristic of a population
Data
1. Qualitative: Attribute
2. Quantitative: Numerical (discrete & continuous)
Levels of measurement
1. Nominal (lowest level)
2. Ordinal
3. Interval
4. Ratio (highest level)
Nominal
-Labels or names
-No order
-Can only be classified and counted
(Ex: classification of the 6 M&M colors)
Ordinal
-Relative ranking or rating of items based on a defined attribute or qualitative variable.
-Only ranked or counted
(Ex: ranking the top 10 states that have the best business climate)
Interval
-The distance between values is meaningful
-Based on a scale with a known unit of measurement
(Ex: Fahrenheit temperature scale)
Ratio
-Based on a scale with a known unit of measurement and a meaningful interpretation of zero on the scale
(Ex: Wages, weight, height, distance, changes in stock price)
Outlier
Extreme Value
-effects mean
Empirical Rule
-For a symmetrical, bell-shaped frequency distribution, approximately 68% of the observations will lie within 1 standard deviation of the mean.
- 95% of the observations will lie within 2 standard deviations of the mean
- 99.7 (practically all) will lie within 3 standard deviations of the mean
Chebyshev's Theorem
-For any set of observations (sample or population), the proportion of the values that lie within k standard deviations of the mean is at least 1 - 1/k^2, where k is any value greater than 1
(determines the minimum proportion of the values that lie within a specified number of standard deviations of the mean)
Skewness
A measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.
Skewed Left
Skewed Right
Normal Distribution
The probability distribution of a continuous random variable.
-bell shaped
-symmetrical
-asymptotic (doesn't touch x axis)
*Location is determined by the mean
*Dispersion/shape is determined by the standard deviation
"Family" of normal distribution
not one single normal distribution
Random Variable
A quantity resulting from an experiment that, by chance, can assume different values.
(Ex: coin toss, random variable is the number of time head results)
discrete random variable
A random variable that can assume only certain clearly separated values. (distance between the values)
(Ex: scores for figure skating. Can be awarded an 8.3 or an 8.4. The space between 8.3 and 8.4 makes this a discrete random variable because a score cannot be 8.365)
Continuous random variable
-Can assume one of an infinite number of values
(Ex: The times of commercial flights between atlanta and LA are 4.67 hours, 5.13 hours, etc. The random variable is the time in hours.)
Probability Distribution
A listing of all the possible outcomes of an experiment and the probability associated with each outcome
Standard normal distribution (also called a Z distribution)
Mean = 0
Standard Deviation = 1
z-score
The distance from the mean, measured in units of the standard deviation
Sampling distribution of the sample mean (ch.8, pg.258)
A probability distribution of all possible sample means of a given sample size.
3 things we learn from the relationship between the population distribution and the sampling distribution of the sample mean:
1. The mean of the sample means equals the population mean
2. The dispersion of the sampling distribution of the sample means is narrower than the population distribution
3. The sample means will follow a normal distribution if one of two things occurs :
-1. population is normal
-2. sample size is large (central limit theorem tells us this)
Central Limit Theorem (pg. 262)
If all samples of a particular size are selected from any population, the sampling distribution of the sample mean is approximately a normal distribution.
-This approximation improves with larger samples
Confidence intervals
A range of values constructed from sample data so that the population parameter is likely to occur within that range at a specified probability (level of confidence).
point estimate
The statistic, computed from sample information, that estimates a population parameter.
(pest single value estimate of the unknown pop parameter)
interval estimate
AKA: confidence interval.
interval that includes the parameter being estimated
standard error (pg. 268)
Standard deviation of the sampling distribution
Margin of error
The precision of the estimate is determined by:
1. The level of confidence (increased level on confidence = lowered precision)
2. variability in the population
3. size of the sample (more info = more precise)
Z distribution
When Standard deviation is known
-Continuous probability distribution
-symmetric (bell shaped)
-mean = 0
T distribution
When standard deviation is not known
3 ways it's the same as Z distribution
-Continuous probability distribution
-symmetric (bell shaped)
-mean = 0
1 way its different:
-More variability than a Z distribution
degrees of freedom
n - 1
Finite Population correction factor
(pg. 304)
For a finite population, where the total number of objects or individuals is N and the number of objects or individuals in the sample is n, we need to adjust the standard errors in the confidence interval formulas.
Continuity Correction Factor
the value .5 is subtracted or added, depending on the question, to a selected value when a discrete probability distribution is approximated by a continuous probability distribution.
Hypothesis
A statement about a population parameter subject to verification
Hypothesis Testing
A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement.
Null Hypothesis
A statement about the value of a population parameter developed for the purpose of testing numerical evidence
Alternate (research) hypothesis
A statement that is accepted if the sample data provide sufficient evidence that the null hypothesis is false.
Test Statistic
A value, determined from sample information, used to determine whether to reject the null hypothesis
rejection region (critical value)
The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected.
level of significance
alpha level
The probability of rejecting the null hypothesis when it is true
p-value
The probability of observing a sample value as extreme as, or more extreme than, the value observed, given that the null hypothesis is true
Type I Error
-Rejecting the null when it is true
5% chance of making a type 1 error
Type II Error
-Not rejecting the null when it is false
Testing Process
1. Null
2. Alternate
3. Test Statistic
4. Rejection region/P-value
5. Decision
6. Answer
Proportion
the fraction, ratio, or percent indicating the part of the sample or the population having a particular trait of interest
mean
quantitative
t
(use when standard deviation is unknown)
proportion
qualitative
z
Median equation
(n+1)/2
simple random sample
a sample selected so that teach item or person in the population has the same chance of being included
systematic random sample
a random staring point is selected, and then every kth member of the population is selected
stratified random sample
a population is divided into subgroups, called strata, and a sample is randomly selected from each stratum
cluster sampling
populations is divided into clusters using naturally occurring geographic or other boundaries, then, clusters are randomly selected and a sample is collected by randomly selecting from each sample
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