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Link Between Confidence Intervals and Hypothesis Testing quiz

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  • How can you test claims about population means besides hypothesis testing?
    You can test claims about population means by building a confidence interval.
  • What does it mean if the claimed mean is outside the 95% confidence interval in a two-tailed test?
    It means you reject the null hypothesis and conclude the claimed value isn't true.
  • What is the critical value z for a 95% confidence interval?
    The critical value z is 1.96 for a 95% confidence interval.
  • How do you calculate the margin of error (E) for a confidence interval for the mean?
    The margin of error E is calculated as z times sigma divided by the square root of n.
  • If the claimed value is not in the confidence interval, what conclusion do you make?
    You reject the claim that the population mean equals the claimed value.
  • What is the formula for alpha in terms of the confidence level?
    Alpha is equal to one minus the confidence level.
  • What are the null and alternative hypotheses for a two-tailed test about a mean?
    The null hypothesis is that mu equals the claimed value, and the alternative is that mu does not equal the claimed value.
  • How do you determine the rejection region in a two-tailed hypothesis test?
    The rejection region is to the left of negative z critical and to the right of positive z critical.
  • What is the test statistic formula for a hypothesis test about a mean?
    The test statistic is (sample mean minus claimed mean) divided by (sigma divided by the square root of n).
  • If your test statistic falls in the rejection region, what do you conclude?
    You reject the null hypothesis.
  • How do the results of a confidence interval and a hypothesis test compare when testing the same claim?
    They lead to the same conclusion about rejecting or not rejecting the claim.
  • In a left-tailed test, when would you reject the null hypothesis using a confidence interval?
    You reject the null if the claimed value is entirely above the confidence interval.
  • In a right-tailed test, when would you reject the claimed value using a confidence interval?
    You reject the claim if the claimed value is entirely below the confidence interval.
  • For which parameters do confidence intervals work well for testing claims?
    Confidence intervals work well for population means (mu) and standard deviations (sigma).
  • Why should you be cautious when using confidence intervals to test claims about population proportions?
    Because building a confidence interval for proportions doesn't always work as intended for hypothesis testing.