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Introduction to Confidence Intervals quiz #2

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  • What is the impact of large samples on the p-value in hypothesis testing?
    Large samples tend to produce smaller p-values if an effect exists, increasing the likelihood of detecting statistical significance.
  • If the confidence level is C%, how do you find alpha?
    Alpha (α) is calculated as α = 1 - C, where C is the confidence level expressed as a decimal.
  • What does the confidence interval suggest about the effectiveness of a treatment?
    If the confidence interval for a treatment effect does not include zero (or the value indicating no effect), it suggests the treatment is effective at the given confidence level.
  • What is the correct formula for the n-period weighted moving average?
    The n-period weighted moving average is calculated as the sum of each observation multiplied by its assigned weight, divided by the sum of the weights.
  • What provides information about the statistical validity of a study?
    The confidence interval and its associated confidence level provide information about the statistical validity of a study's estimate.
  • Which criteria are necessary conditions for making a statistical inference?
    Random sampling, appropriate sample size, and correct statistical methods are necessary for making valid statistical inferences.
  • For a specific confidence level, how do you find the corresponding critical z value?
    For a given confidence level C, calculate α = 1 - C, then α/2, and find the z value with cumulative probability 1 - α/2.
  • Assuming a 90% confidence level, what is the approximate margin of error formula?
    The margin of error is approximately z* × (standard error), where z* ≈ 1.645 for a 90% confidence level.
  • Each t distribution is identified by its ______.
    Each t distribution is identified by its degrees of freedom.
  • What is the level of significance of a test of hypothesis?
    The level of significance (alpha, α) is the probability of rejecting the null hypothesis when it is true.
  • How does a decrease in confidence level affect the sample size required?
    A decrease in confidence level reduces the required sample size for a given margin of error.
  • If the confidence level is C%, how do you find alpha?
    Alpha (α) is found by subtracting the confidence level from 1: α = 1 - C (with C as a decimal).
  • What does the confidence interval suggest about the effectiveness of a treatment?
    If the confidence interval for the treatment effect excludes the value indicating no effect, it suggests the treatment is effective at the specified confidence level.
  • A hypothesis test has a significance level of 10%. What does this significance level represent?
    A 10% significance level means there is a 10% probability of rejecting the null hypothesis when it is actually true (Type I error).
  • In order to make statistical inferences when testing a population parameter, what is required?
    To make statistical inferences, you need a representative sample, appropriate statistical methods, and knowledge of sampling variability.
  • By the empirical rule, how many students in a class of 200 would score within the range μ ± 2σ?
    By the empirical rule, about 95% of students would score within μ ± 2σ, so approximately 190 students in a class of 200.
  • What is the interpretation of a 96% confidence level?
    A 96% confidence level means that if the procedure were repeated many times, about 96% of the resulting intervals would contain the true parameter.
  • In analysis of variance (ANOVA), what is measured by the MS values?
    In ANOVA, MS (mean square) values measure the average variability within and between groups.
  • What is the critical region in hypothesis testing?
    The critical region is the set of values for the test statistic that leads to rejection of the null hypothesis.
  • In interval estimation, as the sample size becomes larger, what happens to the interval estimate?
    As sample size increases, the interval estimate (confidence interval) becomes narrower.
  • How do you express a confidence interval in the form of point estimate ± margin of error?
    A confidence interval is expressed as: point estimate ± margin of error.
  • What does the central limit theorem say?
    The central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.