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Introduction to Statistics: Concepts and Applications, Exams of Statistics

Southern University System (SUS)Statistics

A wide range of fundamental concepts in introductory statistics, including discrete and continuous random variables, parameters and statistics, types of inference, the binomial experiment, categorical and quantitative variables, probability distributions, sampling methods, and visual displays of data. The comprehensive coverage of these topics provides a solid foundation for understanding statistical principles and their applications. The document delves into key formulas, definitions, and examples, making it a valuable resource for students seeking to master the core elements of introductory statistics. Whether you're preparing for an exam, reviewing lecture notes, or seeking a deeper understanding of statistical concepts, this document offers a concise yet informative overview of the essential topics in this field.

Typology: Exams

2023/2024

Available from 08/25/2024

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Straighterline Introduction to Statistics
Exam 2024/2025
1. Discrete random variable
2. Continuous random variable - ANSWER-1. things we count
2. things we measure
1. Parameter
2. Statistic - ANSWER-1. Number that describes the population
2. Number that is computed from the sample
1. Usual
2. Unusual - ANSWER-1. Within two standards deviations of the mean
2. More than two standard deviations above or below the mean
3 Types of inference in this course - ANSWER-Point estimation
Interval Estimation
Hypothesis Testing
Association (does/does not) imply causation. - ANSWER-Does not
Binomial Experiment - ANSWER-1. a fixed number of trials (notation: n trials)
2. each trial must be independent of the others
3. each trial has two possible outcomes, called "success" (the outcome of interest) and
"failure"
4. there is a constant probability (p) of success for each trial, the complement of which
is the probability (1 - p) of failure
Binomials
The Number of outcomes with x successes out of n trials (formula) - ANSWER-[n!]/[x!
*(n-x)!]
Categorical variable - ANSWER-places individuals into one of several groups
Two types: nominal and ordinal
Center of a random variable distribution is measured by its - ANSWER-mean
Cluster Sampling - ANSWER-Used when the population is naturally divided into groups.
Take a random sample of clusters and use all individuals within those clusters as the
sample.
Conditional probability
P(B | A) - ANSWER-the conditional probability of event B occurring given that event A
has occurred
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Straighterline Introduction to Statistics

Exam 2024/

  1. Discrete random variable
  2. Continuous random variable - ANSWER-1. things we count
  3. things we measure
  4. Parameter
  5. Statistic - ANSWER-1. Number that describes the population
  6. Number that is computed from the sample
  7. Usual
  8. Unusual - ANSWER-1. Within two standards deviations of the mean
  9. More than two standard deviations above or below the mean 3 Types of inference in this course - ANSWER-Point estimation Interval Estimation Hypothesis Testing Association (does/does not) imply causation. - ANSWER-Does not Binomial Experiment - ANSWER-1. a fixed number of trials (notation: n trials)
  10. each trial must be independent of the others
  11. each trial has two possible outcomes, called "success" (the outcome of interest) and "failure"
  12. there is a constant probability (p) of success for each trial, the complement of which is the probability (1 - p) of failure Binomials The Number of outcomes with x successes out of n trials (formula) - ANSWER-[n!]/[x! *(n-x)!] Categorical variable - ANSWER-places individuals into one of several groups Two types: nominal and ordinal Center of a random variable distribution is measured by its - ANSWER-mean Cluster Sampling - ANSWER-Used when the population is naturally divided into groups. Take a random sample of clusters and use all individuals within those clusters as the sample. Conditional probability P(B | A) - ANSWER-the conditional probability of event B occurring given that event A has occurred

P(B | A) = P(A and B) / P(A). Confidence intervals for the population mean - ANSWER-Xhat ± z∗⋅[σ/(√n)] Experiment - ANSWER-researchers "take control" of the values of the explanatory variable because they want to see how changes in the value of the explanatory variable affect the response variable Finding an outlier using IQR - ANSWER-An observation is considered a suspected outlier if it is: less than Q1 - 1.5(IQR), or more than Q3 + 1.5(IQR). Four steps in the process of statistics - ANSWER-1. Producing Data

  1. Exploratory Data Analysis
  2. Probability
  3. Inference General Addition Rule - ANSWER-P(A or B) = P(A) + P(B) - P(A and B) used to find events of the type events of the type "A or B" General formula of confidence intervals - ANSWER-point estimation +- margin of error General Multiplication Rule - ANSWER-P(A and B) = P(A) * P(B | A) Used for events of the type "A and B" or when A and B are independent: P(A and B) = P(A) * P(B) In Point Estimation, Estimate the population proportion using the ________, and the population mean using the _______. - ANSWER-Sample proportion, sample mean Interpreting scatterplots:
  4. positive relationship displays as
  5. negative relationship displays as - ANSWER-1. upward slope
  6. downward slope Interpreting Scatterplots: Extrapolation - ANSWER-Prediction for ranges of the explanatory variable that are not in the data; is not reliable and should be avoided Interpreting Scatterplots: How to tell if a linear relationship is strong or weak - ANSWER-closer to -1 is a strong negative linear relationship

Probability distribution - ANSWER-a list of a variable's possible values and their corresponding probabilities Probability sampling plan - ANSWER-any sampling plan that relies on random selection (avoids bias). Quantitative Variable - ANSWER-represents a measurement or a count Two types: Interval and ratio Ratio Variable - ANSWER-quantitative variables for which it makes sense to talk about the difference between values AND the ratio between values; 0 represents the absence of quantity Rules for the linear transformation of one random variable - ANSWER-μ(a+b)X=a+b μX σ^2a+bX=b^2σ^2X Sample surveys - ANSWER-a particular type of observational study in which individuals report variables' values themselves, frequently by giving their opinions. Simple Random Sampling - ANSWER-Every member of the population has an equal probability of being selected for the sample Simpson's paradox - ANSWER-When a lurking variable causes you to rethink the direction of an association Spread of a random variable distribution is measured by its - ANSWER-variance or standard deviation Standard deviation of all sample means - ANSWER-σ/(√n) Standard deviation of all sample proportions - ANSWER-√{[p(1−p)]/n}. Standard Deviation Rule - ANSWER-Approximately 68% of observations fall within 1 sd of the mean, 95% within 2 sd, 99.7% (or virtually all) within 3 sds Stratified sampling - ANSWER-Used when the population is naturally divided into sub- populations called stratum. Choose a simple random sample from each stratum and use these together as the sample. The Complement Rule - ANSWER-P(not A) = 1 - P(A) useful for finding events of the type "at least one of..." Various values of z for different levels of confidence - ANSWER-90%= 1.645 times the standard deviation of sample mean

· 95%= 2 (or precisely 1.96) times the standard deviation of sample mean · 99%= 2.576 times the standard deviation of sample mean Visual display and numerical summary for a single categorical variable - ANSWER-pie chart or bar chart and category percentages Visual display and numerical summary for a single quantitative variable - ANSWER- histogram or stemplot and descriptive statistics Visual display and numerical summary for C->C - ANSWER-Two way table and conditional percentages Visual display and numerical summary for C->Q - ANSWER-Side by side box plots and descriptive statistics Visual display and numerical summary for Q->Q - ANSWER-Scatterplot and correlation coefficient (r) What type of variable?: eye color - ANSWER-nominal What type of variable?: Income - ANSWER-Ratio What type of variable?: socioeconomic status with categories low, med, high - ANSWER-Ordinal What type of variable?: Temperature - ANSWER-Interval z-score for normal random variable - ANSWER-z=(x−μ)/σ