Introduction to Estimation and Confidence Interval in Statistics
30 Questions
0 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 goal of estimation in statistics?

  • To eliminate all errors in calculating the population parameter
  • To provide a best guess at the population parameter with a calculated degree of error (correct)
  • To provide a range of values for the population parameter
  • To provide an exact value of the population parameter

    • What distinguishes point estimation from interval estimation?

  • Interval estimation is used when the sample size is very small.
  • Point estimation provides a range of values, while interval estimation gives one single value.
  • Point estimation provides a single sample value as an estimate, while interval estimation gives a range of values. (correct)
  • Point estimation is more accurate than interval estimation.

    • What does it mean for an estimator to be unbiased?

  • The estimator is always consistent regardless of sample size.
  • The estimator provides the exact population parameter without any error.
  • The expectation of the estimator is equal to the population parameter. (correct)
  • The estimator has the smallest variance among all estimators.

    • In terms of variance, what is expected from a good estimator?

    <p>A good estimator should have minimum variance among all estimators.</p> Signup and view all the answers

    What property ensures that an estimator approaches the true parameter as sample size increases?

    <p>Consistency</p> Signup and view all the answers

    Which type of estimation provides a statement of confidence that the interval contains the population parameter value?

    <p>Interval estimation</p> Signup and view all the answers

    What is the sample mean in the provided text?

    <p>32</p> Signup and view all the answers

    Which value represents the T table value in the text?

    <p>1.833</p> Signup and view all the answers

    What is the range for the confidence interval of the mean expenses per family as per the text?

    <p>29.038 ≤ μ ≤ 34.962</p> Signup and view all the answers

    In what way are the standard error of sampling distribution of sample mean and proportion related to the sample size n?

    <p>They are inversely proportional to n</p> Signup and view all the answers

    What determines the size of a sample according to the text?

    <p>Resources available in terms of time and money</p> Signup and view all the answers

    When estimating the population mean with an error not exceeding a fixed value, what should be the relationship between the sample mean and µ ± E?

    <p>$ar{x} = µ ± E$</p> Signup and view all the answers

    What is a statistical hypothesis?

    <p>A claim about an unknown population parameter value</p> Signup and view all the answers

    What is the methodology that enables a decision-maker to draw inferences about population characteristics?

    <p>Hypothesis testing</p> Signup and view all the answers

    In hypothesis testing, what is the statistic used to test a hypothesis called?

    <p>Test statistic</p> Signup and view all the answers

    What does the level of significance of a test represent?

    <p>Probability that observed difference is due to chance</p> Signup and view all the answers

    What is the purpose of establishing a critical or rejection region in hypothesis testing?

    <p>To decide whether to accept or reject the null hypothesis</p> Signup and view all the answers

    What type of test is described by an alternative hypothesis that provides two-sided alternatives to the null hypothesis?

    <p>Two-tailed test</p> Signup and view all the answers

    What does it mean for an estimator to be efficient?

    <p>It has minimum variance among other unbiased estimators</p> Signup and view all the answers

    What is the key characteristic of a Uniformly Minimum Variance Unbiased Estimator (UMVUE)?

    <p>It is unbiased and has the least variance among other unbiased estimators</p> Signup and view all the answers

    For a 95% confidence interval estimate, what is the value of Zc to be used?

    <p>1.96</p> Signup and view all the answers

    In interval estimation, what does the margin of error represent?

    <p>The range within which the parameter is expected to lie</p> Signup and view all the answers

    What is crucial for determining the confidence interval estimate of a population parameter?

    <p>The sample size</p> Signup and view all the answers

    In constructing a confidence interval, what does a higher level of confidence imply?

    <p>Higher degree of certainty in the estimate</p> Signup and view all the answers

    Which error in hypothesis testing involves rejecting the null hypothesis when it is actually true?

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

    In hypothesis testing, what does a right-tailed test compare the population mean to?

    <p>Greater than a specific value</p> Signup and view all the answers

    What assumption is made when conducting hypothesis testing with large samples (n ≥ 30)?

    <p>Normal distribution of the population</p> Signup and view all the answers

    When does the Central Limit Theorem not guarantee that the sampling distribution of a sample statistic is normal?

    <p>For small sample sizes (less than 30)</p> Signup and view all the answers

    What do Type II errors in hypothesis testing refer to?

    <p>Error of accepting the null hypothesis when it is false</p> Signup and view all the answers

    What do independent random samples drawn from two populations allow in hypothesis testing?

    <p>Testing for difference in means between populations</p> Signup and view all the answers

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser