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Performing Hypothesis Tests: Variance quiz

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  • What is the test statistic used for hypothesis testing of population variance?
    The test statistic is a chi-square value calculated using the formula (n-1)s²/σ².
  • How do you calculate degrees of freedom for a chi-square test of variance?
    Degrees of freedom are calculated as n minus 1, where n is the sample size.
  • What are the null and alternative hypotheses when testing if variance is greater than a specific value?
    The null hypothesis is σ² equals the specified value, and the alternative hypothesis is σ² greater than that value.
  • What must you check before drawing conclusions from a variance hypothesis test?
    You must check that the sample is random and the data are normally distributed.
  • How do you find the sample variance if only the sample standard deviation is given?
    Square the sample standard deviation to obtain the sample variance.
  • What does a p-value less than the significance level α indicate in a variance hypothesis test?
    It indicates you should reject the null hypothesis in favor of the alternative hypothesis.
  • What is the formula for the chi-square test statistic in variance testing?
    The formula is (n-1)s²/σ², where s² is the sample variance and σ² is the hypothesized population variance.
  • What is the significance level α used for in hypothesis testing?
    It is the threshold for deciding whether to reject the null hypothesis based on the p-value.
  • What type of probability do you use for a 'greater than' alternative hypothesis in a chi-square test?
    You use the right-tailed probability of the test statistic.
  • What are the two main assumptions for a valid hypothesis test of variance?
    The sample must be random and the data must be normally distributed.
  • If the sample size is 30, what are the degrees of freedom for the chi-square test?
    The degrees of freedom are 29.
  • What is the purpose of comparing the p-value to α in hypothesis testing?
    To determine whether to reject or fail to reject the null hypothesis.
  • What is the null hypothesis if you want to test if variance is no greater than 0.25?
    The null hypothesis is σ² equals 0.25.
  • What is the alternative hypothesis if you want to test if variance is greater than 0.25?
    The alternative hypothesis is σ² greater than 0.25.
  • Why is it important to check if data are normally distributed in variance hypothesis testing?
    Because the chi-square test for variance assumes normality for valid results.