Skip to main content
Back

Goodness of Fit Test quiz

Control buttons has been changed to "navigation" mode.
1/15
  • What is the purpose of a goodness of fit test?
    A goodness of fit test determines if observed frequencies match expected frequencies based on a claimed distribution.
  • How are observed frequencies defined in a goodness of fit test?
    Observed frequencies are the actual counts seen in the data for each category.
  • What does the null hypothesis state in a goodness of fit test?
    The null hypothesis states that observed frequencies match the claimed distribution.
  • What is the alternative hypothesis in a goodness of fit test?
    The alternative hypothesis states that at least one observed frequency does not match the claimed distribution.
  • What test statistic is used in a goodness of fit test?
    The chi-squared statistic is used, calculated as Σ(O-E)^2/E.
  • How do you calculate expected frequencies when probabilities are equal?
    Expected frequencies are calculated as the sample size divided by the number of categories (E = n/k).
  • How do you calculate expected frequencies when probabilities are unequal?
    Expected frequencies are calculated by multiplying the sample size by the probability for each category (E = n × p).
  • What is the formula for degrees of freedom in a goodness of fit test?
    Degrees of freedom are calculated as the number of categories minus one (df = k - 1).
  • How is the p-value interpreted in a goodness of fit test?
    A low p-value indicates the observed data is unusual under the claimed distribution, suggesting a poor fit.
  • What happens if the p-value is less than the significance level (alpha)?
    If the p-value is less than alpha, you reject the null hypothesis and conclude the observed frequencies do not fit the claimed distribution.
  • What are the conditions that must be met to use a goodness of fit test?
    You need random samples, observed frequencies for all categories, and expected values of at least 5 for each category.
  • What does a high chi-squared value indicate about the data?
    A high chi-squared value indicates a large discrepancy between observed and expected frequencies.
  • How do you calculate the chi-squared statistic for each category?
    For each category, subtract the expected frequency from the observed, square the result, and divide by the expected frequency.
  • What is Benford's Law and how does it relate to goodness of fit tests?
    Benford's Law describes a non-uniform distribution of digits in real-world data, and goodness of fit tests can check if observed data follows this law.
  • What is the final step in a goodness of fit test after calculating the chi-squared statistic?
    The final step is to compare the p-value to the significance level and make a conclusion about the fit between observed and expected frequencies.