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1

descriptive statistics

consists of organizing and summarizing data and describes data through numerical summaries, tables, and graphs.

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inferential statistics

uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result

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population

the entire group of people/objects to be studied

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sample

a subset of the population being studied

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simple random sampling

a sample completed in a way that every sample of size n has an equal chance of being selected

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discrete variable

one that takes on a finite or countably infinite values: no decimal/fractions, Ex. number of siblings, number of dual credits taken, etc.

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continuous variable

takes on an infinite values - decimals/fractions Ex. time, temperature, height, weight, etc.

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Distribution Shapes

bell-shaped, uniform, right-skewed, left-skewed

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Measures of Center

mean, median, mode,

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measures of variation

range, standard deviation, variance, inter-quartile range

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standard deviation

descriptive measure that describes the overall spread of a data set from the mean

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resistant measures

descriptive measures that are not impacted by extremes, Ex. median, mode, inter-quartile range

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left skewed

the mean would be less than the median (extreme values impact the mean)

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bell shaped

the mean would be equal to the median

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right skewed

the mean would be greater than the median (extreme values impact the mean)

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Approximately 68% of the data falls within

1 standard deviation of the mean

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Approximately 95% of the data falls within

2 standard deviations of the mean

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Approximately 99.7% of the data falls within

3 standard deviations of the mean

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parameter

a descriptive measure for a population

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statistic

a descriptive measure for a sample

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z-score

tells you the number of standard deviations an observation is from the mean of the data set.

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mutually exclusive events

two or more events that do not have any outcomes in common or they cannot happen at the same time.

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independent events

Events A and B are independent if P(A) = P(A/B) or P(B) = P(B/A)

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permutation

An ordered arrangement in which r objects are chosen from n distinct (different) objects so that r < n and repetition is not allowed: Use nPr

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combination

A collection, without regard to order, in which r objects are chosen from n distinct objects with r < n and without repetition: Use nCr

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empirical rule for binomial experiments - unusual events

np(1-p) > 10, Unusual if it falls outside of the 2 standard deviation range

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linear correlation coefficient - r

measure of the strength and direction of the linear relation between two quantitative variables - the closer the value r is to 1 the stronger the positive/negative linear correlation

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**coefficient of determination** - r^2

the percent of variation in the y variable that can be explained by the variation in the x variable

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least squares regression line

the line that minimizes the sum of the squared errors (or residuals).

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interpretation of slope

As the x variable changes by 1 unit the y variable changes by the value of the slope in your equation.

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\n **interpretation of y-intercept**

the value of y when x = 0. To interpret you must have x values close to zero and it needs to make sense for the problem

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normally distributed variable

bell shaped - centered at the mean within + and - 3 standard deviations

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standard normal distribution

the z distribution - centered at 0, bell shaped, the mean is 0 and standard deviation 1

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sampling error

the error resulting from using a sample to estimate a population characteristic.

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relation between sample size and sampling error

As the sample size increases, the precision increases (the width of the C. I. decreases)

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Central Limit Theorem

if X is not normally distributed then the Central Limit Theorem states x-bar will be normally distributed if the sample size n 30.

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point estimate

the value of a statistic used to estimate a parameter - x bar, p hat

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relation between confidence and precision

As the confidence level increases the precision decreases (the width of the C.I. interval is increases)

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margin of error

the distance from the point estimate to the end of the confidence interval

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interpretation of a confidence interval

We are _______% confident that the population mean/proportion (describe the variable) is between __________ and __________.

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