Inferential Statistics and Hypothesis Testing
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Questions and Answers

What is the typical level of significance (alpha) used in social sciences?

  • 2.5%
  • 10%
  • 5% (correct)
  • 1%

    • What does a level of significance (alpha) of 0.05 indicate regarding the null hypothesis ($H_0$)?

  • The probability of the null hypothesis being true is less than 5%.
  • The probability of falsely accepting the null hypothesis is 5%.
  • The probability of the null hypothesis being true is always 5%.
  • The probability of falsely rejecting the null hypothesis is no more than 5%. (correct)

    • What is a Type 1 error in hypothesis testing?

  • Incorrectly calculating the probability of rejecting the null hypothesis.
  • Failing to reject a null hypothesis that is actually false.
  • Placing the rejection region in the wrong tail of the distribution.
  • Rejecting a null hypothesis that is actually true. (correct)

    • What does 'power' refer to in the context of hypothesis testing?

    <p>The probability of rejecting a false null hypothesis.</p> Signup and view all the answers

    A Type 3 error occurs when:

    <p>We fail to reject a null hypothesis because we positioned the rejection region in the wrong tail.</p> Signup and view all the answers

    What is the primary purpose of using inferential statistics?

    <p>To make inferences about a population based on sample data.</p> Signup and view all the answers

    According to the information provided, what does the null hypothesis (H0) represent?

    <p>A statement about a population parameter assumed to be true.</p> Signup and view all the answers

    What do tests of significance help determine?

    <p>The likelihood that a hypothesis about a population parameter is true.</p> Signup and view all the answers

    If the null hypothesis is rejected, what does this typically suggest about the alternative hypothesis (H1)?

    <p>It becomes more credible.</p> Signup and view all the answers

    What is the correct approach to significance testing, according to the content provided?

    <p>Assume H0 is true, and see how (un)likely the sample data is under that assumption.</p> Signup and view all the answers

    How is the sample mean related to the population mean, according to the text?

    <p>The sample mean is an unbiased estimator of the population mean.</p> Signup and view all the answers

    What are hypothesis about?

    <p>They are about population parameters.</p> Signup and view all the answers

    What is an alternative hypothesis (H1)?

    <p>A hypothesis that directly contradicts the null hypothesis.</p> Signup and view all the answers

    What is the primary purpose of a two-independent-sample t-test?

    <p>To compare the means of two independent groups.</p> Signup and view all the answers

    Which of the following statements accurately describes the relationship between the estimated standard error and the likelihood of retaining the null hypothesis?

    <p>A higher estimated standard error increases the likelihood of retaining the null hypothesis.</p> Signup and view all the answers

    What is the significance of the 'df' stated as 'df = sum of the dfs = df1 + df2' in the context of the two-independent-sample t-test?

    <p>It represents the degrees of freedom used to determine the critical value for the t-test.</p> Signup and view all the answers

    When would you use a directional hypothesis (H1) in a two-independent-sample t-test?

    <p>When you have a specific prediction about which group will have a higher mean.</p> Signup and view all the answers

    Under what condition is the equal variance assumption usually satisfied in a two-independent-sample t-test?

    <p>When the variance of the larger sample is not greater than twice the variance of the smaller sample.</p> Signup and view all the answers

    How does the size of the t-value affect the p-value in a two-tailed hypothesis (H1) test?

    <p>A larger t-value will result in a smaller p-value.</p> Signup and view all the answers

    Which scenario would increase the likelihood of rejecting the null hypothesis (H0) in a two-tailed t-test?

    <p>Increasing the sample size while keeping other factors constant.</p> Signup and view all the answers

    What is the probability that a randomly selected sample will demonstrate the null hypothesis is false, when the null hypothesis is actually false?

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

    In the context of hypothesis testing, what does H0 represent?

    <p>The null hypothesis</p> Signup and view all the answers

    What is the first step in the manual process of significance testing?

    <p>State H0 and H1</p> Signup and view all the answers

    What happens when the obtained test statistic is greater than the critical value?

    <p>The null hypothesis is rejected.</p> Signup and view all the answers

    What does a critical value represent in hypothesis testing?

    <p>The cutoff value defining the rejection region</p> Signup and view all the answers

    For a two-tailed alternative hypothesis with an alpha of 5%, what is the z-critical value?

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

    What is the purpose of the rejections region?

    <p>To determine when to reject the null hypothesis</p> Signup and view all the answers

    What is the formula to calculate degrees of freedom (df) for a one-sample t-test?

    <p>df = n - 1</p> Signup and view all the answers

    What does a p-value below 0.05 indicate in hypothesis testing?

    <p>We reject H0 and retain H1</p> Signup and view all the answers

    Which of the following accurately describes the relationship between sample size and the t distribution?

    <p>As sample size increases, the t distribution resembles a normal distribution more closely.</p> Signup and view all the answers

    What happens to critical values as sample size increases?

    <p>Critical values become smaller.</p> Signup and view all the answers

    In SPSS, what does a calculated p-value signify?

    <p>It's the probability of obtaining a difference as large as or larger than seen, assuming H0 is true.</p> Signup and view all the answers

    What is the rejection region for a one-tailed hypothesis test at alpha = 5%?

    <p>1.65</p> Signup and view all the answers

    If the obtained value is greater than the critical value, what decision should be made regarding H0?

    <p>We reject H0.</p> Signup and view all the answers

    What should you do with the p-value if the hypothesis is directional?

    <p>Divide it by two.</p> Signup and view all the answers

    What is the primary condition under which a one-independent sample z-test is used?

    <p>The standard deviation is known.</p> Signup and view all the answers

    Which assumption is NOT necessary for a one-independent sample t-test?

    <p>The data must be normally distributed for all sample sizes.</p> Signup and view all the answers

    In the context of hypothesis testing, what does it mean if the z value is higher?

    <p>It becomes more challenging to reject the null hypothesis (H0).</p> Signup and view all the answers

    What is the shape of the sampling distribution when all possible sample means are taken?

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

    Which situation would likely violate the assumption of independence in a one-independent sample t-test?

    <p>Repeated measurements taken from the same individual.</p> Signup and view all the answers

    When is it appropriate to employ a z-test instead of a t-test?

    <p>When the population standard deviation is known.</p> Signup and view all the answers

    What is the role of random sampling in statistical testing?

    <p>It ensures independence between observations.</p> Signup and view all the answers

    In a one-independent sample t-test, what happens to the assumption of normality as the sample size increases past 30?

    <p>It becomes less critical.</p> Signup and view all the answers

    Study Notes

    Inferential Statistics and Hypothesis Testing

    • Inferential statistics allows researchers to learn about populations from samples
    • Sample means are unbiased estimators of population means
    • Central Limit Theorem: sample means follow a normal distribution
    • Hypothesis testing aims to determine if a hypothesis about a population parameter (e.g., mean) is likely to be true based on sample data

    Principles of Hypothesis Testing

    • Significance testing: evaluates the likelihood a hypothesis about a population parameter (like the mean) is true using sample data
    • Null hypothesis (H₀): a statement about a population parameter (often assumed true). It assumes there's no effect or no difference.
    • Alternative hypothesis (H₁ or Hₐ): directly contradicts the null hypothesis; states the parameter has a specific value (often the value expected by a researcher)
    • Significance values/levels (α): threshold for rejecting the null hypothesis (commonly 0.05). 5% chance of falsely rejecting a true null.
    • Alpha (α) = probability of Type I error (rejecting a true null hypothesis).

    Steps in Significance Testing

    • Formulate null hypothesis (HO) and alternative hypothesis (H1), often based on previous research or theory
    • Set a level of significance (alpha)
    • Compute a test statistic (e.g., z-test, t-test)
    • Compare your obtained value with critical value, or determine probability of obtaining results if the null were true (p-value)

    Type I and Type II Errors

    • Type I error: rejecting the null hypothesis when it is actually true.
    • Type II error: failing to reject the null hypothesis when it is actually false.

    One-Sample Z-Test

    • Used when population standard deviation (σ) is known
    • Assumptions: Normality of population, random sampling, independence of outcomes

    One-Sample T-Test

    • Used when population standard deviation (σ) is unknown and is estimated using the sample standard deviation
    • Assumptions: Normality of population, random sampling, and independence of outcomes

    Two-Independent Samples T-Test

    • Used to compare the means of two independent groups.
    • Assumptions: Normality of populations, random sampling, and equal variances between the two groups.
    • Levene's test: assesses if variances are equal between groups.

    Estimation and Confidence Intervals

    • Estimation: using sample data to estimate a population parameter.
    • Point estimation: using a single statistic (e.g., sample mean) to estimate the population parameter.
    • Confidence interval: a range of values likely to contain the population parameter.
    • Confidence Level: the probability that the confidence interval contains the true population parameter.
    • Critical values: critical z values or t values based on confidence level, used for interval estimation.

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    Part 2 PDF - Hypothesis Testing

    Description

    This quiz covers the key concepts of inferential statistics, including hypothesis testing and the Central Limit Theorem. You will gain an understanding of how sample means can provide insights about population parameters and the significance levels used in testing hypotheses. Test your knowledge on null and alternative hypotheses.

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