Business Statistics Chapter 5: Confidence Intervals
27 Questions
2 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the main purpose of confidence interval estimation?

  • To indicate the variability of an estimate (correct)
  • To replace hypothesis testing in statistical analysis
  • To calculate the exact value of a population statistic
  • To provide a single value estimate of a population parameter

    • Which type of estimation provides a range of values to estimate a population parameter?

  • Descriptive statistics
  • Point estimation
  • Interval estimation (correct)
  • Non-parametric testing

    • In hypothesis testing, what is the term for the assumed state before testing?

  • Null hypothesis (correct)
  • Alternative hypothesis
  • Sample hypothesis
  • Parametric hypothesis

    • What statistic is used as the best point estimate for the population mean?

    <p>Sample mean (C)</p> Signup and view all the answers

    Which of the following describes a confidence interval?

    <p>A range of values that likely contains the true population parameter (C)</p> Signup and view all the answers

    What does a 95% confidence level indicate in interval estimation?

    <p>The interval will contain the population parameter in 95 out of 100 samples (A)</p> Signup and view all the answers

    Which of the following is NOT a characteristic of interval estimation?

    <p>It guarantees the population parameter will be within the range (D)</p> Signup and view all the answers

    Why might statisticians prefer interval estimation over point estimation?

    <p>Interval estimation gives additional information about variability (C)</p> Signup and view all the answers

    What is an error that can occur in hypothesis testing?

    <p>Type I error (D)</p> Signup and view all the answers

    Which statement about population and sample statistics is correct?

    <p>Population parameters are known and sample statistics are estimates (C)</p> Signup and view all the answers

    The process of using sample data to make inferences about a population is known as?

    <p>Inferential statistics (C)</p> Signup and view all the answers

    What do confidence intervals and hypothesis tests have in common?

    <p>Both are methods of statistical analysis (D)</p> Signup and view all the answers

    What is the role of a confidence interval in statistical inference?

    <p>To allow estimation of population parameters with uncertainty (D)</p> Signup and view all the answers

    What is the range indicated by a confidence interval?

    <p>The range within which the population parameter likely falls (C)</p> Signup and view all the answers

    Which of the following reflects a typical confidence level used in statistics?

    <p>95% (C)</p> Signup and view all the answers

    What does increasing the sample size affect in the context of confidence intervals?

    <p>It decreases the width of the confidence interval (B)</p> Signup and view all the answers

    In hypothesis testing, what does the null hypothesis typically suggest?

    <p>There is no significant difference between groups (D)</p> Signup and view all the answers

    What is the consequence of a Type I error in hypothesis testing?

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

    What does the term 'level of confidence' refer to?

    <p>The probability that a confidence interval contains the true parameter (A)</p> Signup and view all the answers

    How is the critical value for a normal distribution represented in confidence interval calculations?

    <p>By Z-values (C)</p> Signup and view all the answers

    What should the population distribution look like for using the standard deviation in confidence interval calculations?

    <p>Normally distributed (B)</p> Signup and view all the answers

    What is the formula for estimating the confidence interval when the population standard deviation is known?

    <p>$X ± Z_{α/2} * σ$ (D)</p> Signup and view all the answers

    What is indicated when a confidence interval of 95% is calculated?

    <p>95% of similar samples will contain the true parameter (C)</p> Signup and view all the answers

    Which is true about confidence intervals when a high level of confidence is used?

    <p>The interval will be wider (D)</p> Signup and view all the answers

    Which scenario describes a situation appropriate for hypothesis testing?

    <p>Comparing average heights of two different species (A)</p> Signup and view all the answers

    In the context of hypothesis testing, what role do alternate hypotheses have?

    <p>They compete with the null hypothesis (D)</p> Signup and view all the answers

    What does the notation $α$ represent in statistics?

    <p>The significance level (B)</p> Signup and view all the answers

    Flashcards

    Estimation

    A process of estimating the value of a population parameter from data collected from a sample.

    Point Estimation

    A single number used to estimate a population parameter.

    Interval Estimation

    A range of values that is likely to contain the true population parameter.

    Confidence Level

    A measure of how confident you are that the true population parameter falls within a particular interval.

    Signup and view all the flashcards

    Confidence Interval Estimation

    The process of calculating a confidence interval using sample data.

    Signup and view all the flashcards

    Hypothesis

    A statement that proposes something about a population parameter.

    Signup and view all the flashcards

    Hypothesis Testing

    A process of determining whether enough evidence exists to reject a hypothesis.

    Signup and view all the flashcards

    Null Hypothesis

    A hypothesis about a population parameter that states that the parameter is equal to a specific value.

    Signup and view all the flashcards

    Alternative Hypothesis

    A hypothesis about a population parameter that states that the parameter is different from a specific value.

    Signup and view all the flashcards

    Type I Error

    A type of error in hypothesis testing where the null hypothesis is rejected when it is actually true.

    Signup and view all the flashcards

    Type II Error

    A type of error in hypothesis testing where the null hypothesis is not rejected when it is actually false.

    Signup and view all the flashcards

    Significance Level

    The probability of committing a Type I error.

    Signup and view all the flashcards

    Power of a Test

    The probability of correctly rejecting the null hypothesis when it is false.

    Signup and view all the flashcards

    Critical Region

    A range of values where the sample mean should fall if the null hypothesis is true.

    Signup and view all the flashcards

    T-Test

    A statistical test used to compare the means of two groups.

    Signup and view all the flashcards

    Confidence Interval

    Confidence Interval is a range of values that is likely to contain the true value of a population parameter. It is a measure of how confident we are that the true value falls within the interval.

    Signup and view all the flashcards

    Margin of Error

    The margin of error is the maximum expected difference between the sample statistic and the true population parameter.

    Signup and view all the flashcards

    Factors Affecting Confidence Interval Width

    Factors that influence the width of a confidence interval are sample size, confidence level, and data variability.

    Signup and view all the flashcards

    Assumptions for Confidence Intervals

    Assumptions for confidence intervals are: population is normally distributed; sample size is large (n>30) or population is known to be normally distributed; variance is known.

    Signup and view all the flashcards

    Null Hypothesis (H0)

    A null hypothesis is a statement that there is no difference or no effect.

    Signup and view all the flashcards

    Alternative Hypothesis (H1)

    An alternative hypothesis is a statement that contradicts the null hypothesis, suggesting a difference or effect.

    Signup and view all the flashcards

    p-value

    The p-value, a number between 0 and 1, represents the probability of obtaining the observed results if the null hypothesis were true.

    Signup and view all the flashcards

    Confidence Interval

    A confidence interval is a range of values that is likely to contain the true value of a population parameter. It is a measure of how confident we are that the true value falls within the interval.

    Signup and view all the flashcards

    Statistical Significance

    Statistical Significance refers to the likelihood that a result is not due to random chance.

    Signup and view all the flashcards

    Statistically Significant Outcome

    The concept of a statistically significant outcome implies that the observed result is unlikely to have happened by chance.

    Signup and view all the flashcards

    Signup and view all the flashcards

    Study Notes

    Course Objectives

    • The course focuses on developing practical computing skills and problem-solving abilities in business.
    • Statistical tools and appropriate graphs will be used.
    • Data analysis and interpretation using spreadsheets.

    Chapter 5: Confidence Intervals and Hypothesis Testing

    • The chapter covers confidence interval estimation and hypothesis testing elements.
    • This is part of a Business Statistics course (BSMS2209).
    • The material relates to business administration curriculum requirements.
    • Students will learn the process of estimating confidence intervals of population parameters such as the mean, with specified confidence levels.

    Learning Outcomes-Chapter 5

    • Understanding confidence intervals and hypothesis testing elements
    • Application of concepts through practical examples
    • Correctly applying statistical measures
    • Selecting appropriate graphical representation.

    Detailed Outline

    • Introduction to hypothesis formulation
    • Different types of statistical hypotheses
    • Potential errors during hypothesis testing
    • Introduction to estimation: population and samples
    • Types of estimates, point and interval estimates
    • The concept of confidence level
    • The estimation process
    • Confidence intervals for population means
    • Example: One out of every four Americans currently follow a diet.

    Estimation Introduction

    • Estimation is an aspect of inferential statistics.
    • The process involves estimating a population parameter from sample data.
    • Example: A sample of 70 students from a university shows an average height of 5.4 feet. This is an estimate of the mean height of all students. x (the sample mean = the estimator)

    Point Estimation

    • A point estimate uses a single value to estimate a population parameter.
    • Example: In a sample, the average height of students was 5.4 ft. This is a point estimate for the population mean.

    Interval Estimation

    • An interval estimate provides a range of values likely to contain the population parameter.
    • Indicates the likely interval of values in which the true value lies.
    • Example: The true average student height was described as being between 64 and 66 inches. This estimated interval is a confidence interval.

    Example 1:

    • A random sample (n=3) includes 1, 3, and 5.
      • Compute population mean.
      • Compute population standard deviation.

    Example with calculations.

    • Provides calculations to find the point estimate for a mean and standard deviation. - (Illustrative calculations for x bar and S are provided)

    Example 2:

    • (n=6) Sample elements are: 6, 10, 13, 14, 18, and 20.
      • Compute points estimates of the population mean.
      • Compute population standard deviation

    Confidence Levels

    • The confidence level represents the likelihood of the correct population parameter falling within the calculated interval.
    • Common levels are 90%, 95%, and 99%.

    Confidence Intervals for Population Means

    • Formula for confidence intervals: X ± Zα/2 * (σ/√n)
    • X = sample mean, Zα/2 = critical value from the standard normal distribution (or a table using 'Z-value')
      • σ = population standard deviation
      • n = sample size

    Determining confidence intervals

    • To determine the confidence intervals for the population mean, use the critical value and the sample size, sample standard deviation.

    Applications

    • Calculating confidence intervals for mean height of college students and average miles driven per year by automobiles provide further practical applications.

    Additional Examples

    • Examples on calculating confidence intervals for means.
    • Examples show how to calculate confidence intervals for population mean when standard deviation is known and when it is unknown.

    Hypothesis Testing

    • Concepts of null and alternative hypotheses are presented
    • Explanation of error types in hypothesis testing

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    BSMS2209 CH#5 ESTIMATION AND HYPOTHESIS TESTING -v1 PDF

    Description

    This quiz covers Chapter 5 of the Business Statistics course (BSMS2209), focusing on confidence intervals and hypothesis testing. Students will learn to estimate confidence intervals of population parameters and apply statistical measures appropriately. Practical examples and graphical representations are emphasized.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser