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Goodness of FIt Test Using TI-84 quiz

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  • What is the purpose of a chi-square goodness of fit test?
    It is used to compare observed frequencies to expected values to determine if the observed data fits a claimed distribution.
  • How do you state the null hypothesis in a goodness of fit test?
    The null hypothesis states that the observed frequencies match the claim distribution.
  • What is the alternative hypothesis in a goodness of fit test?
    The alternative hypothesis states that the observed frequencies do not match the claim distribution.
  • How do you calculate expected values when the claim is equal distribution among categories?
    Use the formula e = n / k, where n is the total sample size and k is the number of categories.
  • If 200 people are surveyed about 4 flavors, what is the expected value for each flavor?
    The expected value for each flavor is 200 divided by 4, which equals 50.
  • How do you determine the degrees of freedom for a goodness of fit test?
    Degrees of freedom are calculated as k - 1, where k is the number of categories.
  • What are the steps to enter observed and expected data into a TI-84 for a GOF test?
    Enter observed frequencies in L1 and expected values in L2 using the STAT button.
  • Which menu option on the TI-84 is used for the chi-square goodness of fit test?
    Use option D, the chi-square GOF test, in the TESTS menu.
  • What must you check regarding degrees of freedom when using the TI-84 for a GOF test?
    Ensure the degrees of freedom in the calculator matches your problem, adjusting it if necessary.
  • What key result do you compare to the significance level in a GOF test?
    You compare the p-value to the alpha (significance) level.
  • What does it mean if the p-value is greater than the significance level?
    It means you fail to reject the null hypothesis, indicating insufficient evidence to say the observed frequencies differ from the claim.
  • What does the 'CNTRB' value shown in the TI-84 output represent?
    It shows each observed frequency's contribution to the overall chi-square statistic.
  • If the p-value is 0.44 and alpha is 0.05, what is your conclusion?
    Since 0.44 > 0.05, you fail to reject the null hypothesis and conclude the observed data fits the claim distribution.
  • Why is it important to use the chi-square GOF test (option D) and not just the chi-square test on the TI-84?
    Because the GOF test is specifically designed for comparing observed and expected frequencies across categories.
  • What is the main conclusion if you fail to reject the null hypothesis in a goodness of fit test?
    You conclude that the observed data is consistent with the expected distribution based on the claim.