Statistics Chapter 5: Confidence Intervals & Hypothesis Testing

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Questions and Answers

What is a point estimate?

  • A combination of multiple estimates to predict a population characteristic.
  • A range of values that estimate a population parameter.
  • A single number that estimates a population parameter. (correct)
  • An estimate that guarantees the exact population parameter.

Why do statisticians prefer interval estimates over point estimates?

  • Interval estimates are always larger than point estimates.
  • Interval estimates provide a measure of variability and uncertainty. (correct)
  • Interval estimates are simpler to calculate.
  • Point estimates are more reliable than interval estimates.

Which of the following statements about confidence intervals is true?

  • A confidence interval is a single value that predicts the population mean.
  • Confidence intervals are only useful for small sample sizes.
  • Confidence intervals help assess the accuracy and reliability of point estimates. (correct)
  • A confidence interval does not provide any information about the population.

What is the main purpose of hypothesis testing in statistics?

<p>To make decisions about population parameters based on sample data. (A)</p> Signup and view all the answers

Which of the following describes a confidence interval for a population mean?

<p>It indicates a range within which the population mean is expected to fall. (B)</p> Signup and view all the answers

Which type of hypothesis testing involves parameters that make specific assumptions about population distributions?

<p>Parametric testing (B)</p> Signup and view all the answers

What could be a consequence of relying solely on a point estimate?

<p>It can mislead conclusions due to lack of uncertainty information. (B)</p> Signup and view all the answers

Errors in hypothesis testing primarily refer to what?

<p>Incorrect conclusions drawn about population parameters. (D)</p> Signup and view all the answers

What does a statistical hypothesis represent?

<p>A conjecture about a population parameter. (D)</p> Signup and view all the answers

Which statement best describes the null hypothesis?

<p>It claims that there is no difference between a parameter and a specific value. (D)</p> Signup and view all the answers

What is the primary purpose of hypothesis testing?

<p>To evaluate claims about a population and make decisions. (A)</p> Signup and view all the answers

What distinguishes a parametric test from a nonparametric test?

<p>Parametric tests assume specific population distributions. (D)</p> Signup and view all the answers

Which of the following is true about interval estimates?

<p>They communicate a certain level of confidence about unknown parameters. (D)</p> Signup and view all the answers

What is a type I error in hypothesis testing?

<p>Rejecting the null hypothesis when it is indeed true. (D)</p> Signup and view all the answers

Which of the following is a characteristic of the alternative hypothesis?

<p>It assumes the existence of a difference between parameters. (D)</p> Signup and view all the answers

How can a researcher minimize type II errors?

<p>By increasing sample size. (D)</p> Signup and view all the answers

Flashcards

Estimation

Using sample data to approximate an unknown population characteristic.

Point Estimate

Single numerical value used to estimate a population parameter. Eg: The average age of students in a sample is 22 years. This is a point estimate of the average age of all students.

Confidence Interval

A range of values likely to contain the true population parameter. It provides more info about the uncertainty of the estimate.

Confidence Level

The degree of confidence that the true population parameter lies within the interval. Represented as a percentage.

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Hypothesis

A statement about a population parameter that we want to test. It is a claim about the population that we want to either support or reject.

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Hypothesis Testing

A process used to determine whether there is enough evidence to reject the null hypothesis. This is the statement we are trying to disprove.

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Parametric Test

Statistical techniques that assume the data follows a specific distribution. Eg: t-test, z-test, ANOVA.

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Nonparametric Test

Statistical techniques that don't make assumptions about the data distribution. Eg: Wilcoxon signed-rank test, Kruskal-Wallis test.

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Interval Estimate

An interval estimate of a parameter is a range of values used to estimate the true value of the parameter. It accounts for the variability in sample statistics and provides information about the confidence level for the estimated range.

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Null Hypothesis (Ho)

The null hypothesis (Ho) states that there is no difference or relationship between the variables being studied. It represents the status quo or 'no effect' assumption.

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Alternative Hypothesis (H₁)

The alternative hypothesis (H₁) is a statement that contradicts the null hypothesis. It suggests a specific difference or relationship between variables.

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Type I Error

Type I error occurs when we reject the null hypothesis when it is actually true. We conclude there is a difference or effect when there is not.

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Type II Error

Type II error occurs when we fail to reject the null hypothesis when it is actually false. We conclude there is no difference or effect when there is.

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Study Notes

Chapter 5: Confidence Interval Estimation and Elements of Hypothesis Testing

  • This chapter covers confidence intervals and hypothesis testing in statistics
  • Learning outcome: Examine confidence interval estimation and the elements of hypothesis testing
  • Estimation is a process of estimating a parameter's value using sample data
  • Examples of estimation include: one in four Americans are on a diet, 72% of Americans have flown on commercial airlines, average kindergarten student has seen over 5,000 hours of television.
  • Confidence intervals estimate a range of values likely to contain the true population parameter
  • A point estimate is a single number that estimates a population parameter
  • A confidence interval provides additional information on the estimate’s variability
  • The width of the confidence interval indicates the range of values the population parameter may fall between.
  • Confidence intervals are expressed in terms of probability or level of confidence (e.g., 95% confident)

Chapter 5 Outline

  • Estimation introduction
  • Notations of population and sample
  • Types of estimates
  • Point and interval estimates
  • Hypothesis
  • Hypothesis Testing
  • Types of Statistical Hypotheses
  • Parametric and Nonparametric Tests
  • Errors in Hypothesis Testing

Estimation — Introduction

  • Inferential statistics involve estimation of population characteristics, such as the mean or proportion.

Types of Estimates

  • Point estimates: A single value that represents an estimate of a population parameter. Point estimates can be inaccurate.
  • Interval estimates: Provide a range of values likely to contain the population parameter. Confidence intervals are examples of interval estimates.

Hypothesis

  • A hypothesis is an assumption based on evidence.
  • A hypothesis contains components like variables, populations, and the relationship between variables.
  • A research hypothesis tests the relationship between two or more variables.
  • A statistical hypothesis is a conjecture (assumption) about a population parameter, which may or may not be true

Hypothesis Testing

  • Significance testing evaluates claims about a population
  • Begins with a hypothesis statement

Types of Statistical Hypotheses

  • Null hypothesis (H0): Asserts there is no difference between a parameter and a specific value, or between two parameters.
  • Alternative hypothesis (H1): States that there is a difference between a parameter and a specific value, or between two parameters.

Parametric and Non-parametric Tests

  • Parametric tests: Make assumptions about the population parameters (e.g., normality)
  • Non-parametric tests: Do not require assumptions about the population distributions

Errors in Hypothesis Testing

  • Type I error: Rejecting the null hypothesis when it is true.
  • Type II error: Failing to reject the null hypothesis when it is false.

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Chapter 5: Confidence Interval Estimation and Hypothesis Testing PDF

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