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Goodness of Fit Test quiz #1

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  • What are the necessary conditions to perform a chi-square goodness-of-fit test?
    The necessary conditions are: (1) data are from a random sample, (2) observed frequencies are available for all categories, and (3) expected frequencies for each category are at least 5.
  • For what type of data is a chi-square goodness-of-fit test most appropriate?
    A chi-square goodness-of-fit test is most appropriate for categorical data where you want to compare observed frequencies to expected frequencies based on a claimed distribution.
  • How is the chi-square test statistic for a goodness-of-fit test calculated?
    The chi-square test statistic is calculated as χ² = Σ[(O - E)² / E], where O is the observed frequency and E is the expected frequency for each category.
  • What are the possible values for a chi-square statistic?
    A chi-square statistic can take any value greater than or equal to zero; it cannot be negative.
  • How would you describe the purpose of the chi-square test for goodness of fit?
    The chi-square test for goodness of fit is used to determine whether observed frequencies differ significantly from expected frequencies based on a claimed distribution.
  • What does the null hypothesis specify in a chi-square goodness-of-fit test?
    The null hypothesis specifies that the observed frequencies match the expected frequencies according to the claimed distribution.
  • Which statement is not true about the chi-square goodness-of-fit test?
    It is not true that the chi-square goodness-of-fit test can be used for data with expected frequencies less than 5 in any category.
  • What is the main use of the chi-square goodness-of-fit test?
    The main use is to test whether observed categorical data fit a specified theoretical distribution.
  • Which of the following is not a characteristic of the chi-square distribution?
    The chi-square distribution is not symmetric; it is skewed to the right, especially for small degrees of freedom.
  • What is not a requirement to conduct a chi-square goodness-of-fit test?
    It is not required that the data be numerical or continuous; the test is for categorical data.
  • What is a key property of the chi-square distribution regarding its shape?
    The chi-square distribution is always non-negative and is skewed to the right, becoming more symmetric as degrees of freedom increase.
  • What is a requirement for the expected frequencies in a chi-square goodness-of-fit test?
    Each expected frequency must be at least 5.
  • What is the general process for conducting a chi-square goodness-of-fit test?
    State the hypotheses, check conditions, calculate expected frequencies, compute the chi-square statistic, determine the p-value, and draw a conclusion.
  • How do you find the expected value for each category in a chi-square goodness-of-fit test when the claimed probabilities are equal?
    Divide the total sample size by the number of categories: E = n / k.
  • How do you find the expected value for each category in a chi-square goodness-of-fit test when the claimed probabilities are not equal?
    Multiply the total sample size by the claimed probability for each category: E = n × p (where p is the claimed probability for that category).
  • What is the formula for degrees of freedom in a chi-square goodness-of-fit test?
    Degrees of freedom = number of categories minus one (df = k - 1).
  • How is the null hypothesis typically stated in a chi-square goodness-of-fit test?
    The null hypothesis states that the observed frequencies follow the specified distribution.
  • What happens if the p-value in a chi-square goodness-of-fit test is less than the significance level?
    If the p-value is less than the significance level, you reject the null hypothesis, indicating the observed data do not fit the claimed distribution.
  • What does a large chi-square statistic indicate in a goodness-of-fit test?
    A large chi-square statistic indicates a large discrepancy between observed and expected frequencies, suggesting the data do not fit the claimed distribution well.
  • List the requirements to perform a chi-square goodness-of-fit test.
    The requirements are: (1) data from a random sample, (2) all expected frequencies are at least 5, and (3) observed frequencies are available for all categories.