Statistics Quiz on Variables and Distributions

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Questions and Answers

What is the definition of a variable in statistics?

  • A quantity that can take on different values.
  • A characteristic that is observable or measurable in every unit of the universe. (correct)
  • The average of a data set.
  • A set of all possible outcomes of an experiment.

What is the difference between a discrete random variable and a continuous random variable?

  • A discrete random variable can only take on a finite number of values, while a continuous random variable can take on an infinite number of values. (correct)
  • A discrete random variable is a subset of a sample space, while a continuous random variable is the entire sample space.
  • A discrete random variable is always measured in whole numbers, while a continuous random variable can be measured in fractions.
  • A discrete random variable is always measured with a unit, while a continuous random variable is unitless.

Which of the following is NOT a measure of central tendency?

  • Median
  • Variance (correct)
  • Mode
  • Mean

What does the probability mass function (pmf) represent?

<p>The probability distribution of a discrete random variable. (C)</p> Signup and view all the answers

What is the standard deviation of a normal distribution with a mean of 10 and a variance of 4?

<p>2 (A)</p> Signup and view all the answers

What is the purpose of data collection in statistics?

<p>To gather and measure information on variables of interest in a systematic way to answer research questions. (A)</p> Signup and view all the answers

What is the difference between an event and a sample space?

<p>An event is a subset of a sample space, while a sample space is the set of all possible outcomes. (B)</p> Signup and view all the answers

What does the term 'experiment probability' refer to?

<p>The probability of an event occurring based on the results of an experiment repeated many times. (A)</p> Signup and view all the answers

What is the standard normal distribution characterized by?

<p>A mean of 0 and a standard deviation of 1. (B)</p> Signup and view all the answers

Which of the following is NOT a characteristic of a normal distribution?

<p>Skewed distribution. (A)</p> Signup and view all the answers

What is the name of the distribution used to estimate population parameters when the sample size is small and the population variance is unknown?

<p>Student's T-Distribution (C)</p> Signup and view all the answers

What is the primary importance of the Central Limit Theorem?

<p>It demonstrates that as sample size increases, the sampling distribution of the mean approaches a normal distribution. (D)</p> Signup and view all the answers

Which of the following best describes a parameter?

<p>A measure calculated from the entire population. (B)</p> Signup and view all the answers

What is the purpose of a confidence interval?

<p>To estimate a range of plausible values for a population parameter. (C)</p> Signup and view all the answers

What is the relationship between the Central Limit Theorem and the Student's T-Distribution?

<p>The Central Limit Theorem states that as the sample size increases, the Student's T-Distribution becomes more similar to the standard normal distribution. (B)</p> Signup and view all the answers

Which of these is NOT a characteristic of the normal distribution?

<p>It is a discrete probability distribution. (D)</p> Signup and view all the answers

What is a percentile?

<p>A percentage of the population that falls below a specific score. (D)</p> Signup and view all the answers

What is a 'statistic'?

<p>A measure that describes a characteristic of a sample. (A)</p> Signup and view all the answers

What is the standard normal distribution table used for?

<p>To determine the probability of observing a specific value in a normal distribution. (A)</p> Signup and view all the answers

Who developed the t-distribution and under what alias?

<p>William Sealy Gosset, under the alias 'Student' (D)</p> Signup and view all the answers

Flashcards

Standard Normal Distribution Table

A compilation of areas from the standard normal distribution.

Population

Data set contains all members of a specified group.

Sample

Subset of a population used for analysis.

Parameter

A measure calculated using all data in the population.

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Statistic

A measure calculated using data from a sample only.

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Sampling Distribution

Probability distribution for a sample statistic from repeated random samples.

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Normal Distribution

A bell-shaped curve where mean, mode, and median are center and peak.

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Central Limit Theorem

As sample size increases, the sampling distribution approaches normality.

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Confidence Interval

A range of values used to estimate a parameter's true value.

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Degrees of Freedom

Maximum number of independent values that can vary in a sample.

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Probability

A branch of mathematics dealing with uncertainty and event likelihood.

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Variable

An observable or measurable attribute of a person, place, thing, or idea.

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Data Collection

The process of gathering and measuring information systematically.

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Sample Space

The set of all possible outcomes in a probability experiment.

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Event

A subset of the sample space, representing specific outcomes.

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Experiment Probability

Probability determined from the results of repeated experiments.

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Discrete Random Variable

A variable that can take on a finite number of distinct values.

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Continuous Random Variable

A variable that can assume an infinite number of values in an interval.

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Study Notes

Statistics

  • Science of developing methods for planning experiments, collecting data, analyzing it, interpreting it, and drawing conclusions
  • Deals with uncertainty

Probability

  • Branch of mathematics
  • Measures likelihood of events

Variables

  • Attributes describing people, places, things, or ideas
  • Observable and measurable characteristics

Data Collection

  • Process of gathering information
  • Enables answering research questions, testing hypotheses, and evaluating outcomes
  • Systematically gathers variable data

Sample Space

  • Set of all possible outcomes

Event

  • Subset of a sample space
  • Specific collection of outcomes

Experiment Probability

  • Determined from repeated experiments

Discrete Random Variable

  • Can take a finite (countable) number of distinct values
  • Values are exact, non-negative numbers

Continuous Random Variable

  • Can assume infinite number of values within an interval

Probability Mass Function (PMF)

  • Probability distribution of a discrete random variable

Mean

  • Average of a data set
  • Calculated by adding all numbers and dividing by the count

Variance

  • Statistical measure of data spread around the mean

Standard Deviation

  • Measures dispersion of data relative to the mean
  • Calculated as the square root of variance

Normal Distribution

  • Bell-shaped curve
  • Mean, mode, and median are at the center

Standard Normal Distribution

  • Normal distribution with a mean of 0 and standard deviation of 1

Standard Normal Distribution Table

  • Compilation of areas from the standard normal distribution

Population

  • Complete set of members in a specified group

Sample

  • Subset of a population

Parameter

  • Measure or characteristic from all data values in a population

Sampling Distribution

  • Probability distribution of sample statistics obtained from repeated samples

Normal Distribution

  • Data distribution often observed
  • Characterized by a bell-shaped curve with mean, mode, and median as center

Central Limit Theorem

  • Sampling distribution of the mean approaches a normal distribution as sample size increases

Student's T-Distribution

  • Probability distribution used to estimate population parameters with small sample sizes

William Sealy Gosset

  • Developed the t-distribution
  • Published under the pseudonym "Student"

Percentile

  • Describes how a score compares to others in a set

Confidence Interval

  • Range of values used to estimate a parameter

Narrowness of Confidence Interval

  • Related to the confidence interval's width and length

Degree of Freedom

  • Maximum logically independent values varying in a sample

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