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Critical Values and Rejection Regions quiz

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  • What is the purpose of a critical value in hypothesis testing?
    A critical value marks the threshold between expected and unusual test statistics, helping to determine if the null hypothesis should be rejected.
  • How do you find the critical value for a left-tailed hypothesis test with alpha = 0.05?
    You find the z value with a left tail area of 0.05, which is approximately -1.64.
  • What is the rejection region in a hypothesis test?
    The rejection region is the area beyond the critical value(s) where, if the test statistic falls within it, the null hypothesis is rejected.
  • What is the critical value for a right-tailed test with alpha = 0.05?
    The critical value is approximately 1.64, corresponding to a right tail area of 0.05.
  • How are the critical values determined for a two-tailed test with alpha = 0.05?
    Each tail has an area of 0.025, and the critical values are approximately -1.96 and 1.96.
  • What conclusion do you draw if the test statistic falls inside the rejection region?
    If the test statistic is in the rejection region, you reject the null hypothesis.
  • What is the formula for calculating the z test statistic?
    The formula is z = (x̄ - μ) / (σ / √n), where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
  • How does the critical value method differ from the p-value method in hypothesis testing?
    The critical value method compares the test statistic directly to the critical value, while the p-value method compares the p-value to alpha.
  • What is the critical value for a left-tailed test with alpha = 0.01?
    The critical value is approximately -2.33.
  • If the test statistic is -4.2 and the critical value is -2.33, what is the decision?
    Since -4.2 is less than -2.33 and falls in the rejection region, you reject the null hypothesis.
  • What are the null and alternative hypotheses for testing if a mean is less than a claimed value?
    The null hypothesis is μ = claimed value, and the alternative hypothesis is μ < claimed value.
  • What must be true about the sample size or distribution to use the z test?
    Either the population must be normally distributed, or the sample size n must be greater than 30.
  • What does it mean if the p-value is less than alpha?
    It means there is enough evidence to reject the null hypothesis.
  • How do you determine the rejection region for a two-tailed test?
    The rejection region consists of both tails beyond the negative and positive critical values.
  • Do the p-value and critical value methods always lead to the same conclusion?
    Yes, both methods will lead to the same decision about whether to reject or fail to reject the null hypothesis.