Chi Square Test and Distribution
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Questions and Answers

What does the chi-square formula represent?

  • The sum of squared errors
  • The difference between observed and expected values (correct)
  • The product of observed and expected values
  • The correlation between two variables

    • How is the number of degrees of freedom calculated for the chi-square test statistic?

  • By subtracting one from the product of rows and columns (correct)
  • By subtracting the sample size from the total population
  • By subtracting the number of rows from the number of columns
  • By subtracting the number of categories from the sample size

    • According to the hypotheses mentioned, what does the null hypothesis state?

  • The samples come from the same population
  • All observations are statistically significant
  • There is no difference in distribution among social classes (correct)
  • There is a significant difference in distribution among social classes

    • What is the purpose of calculating the expected value for each cell in a chi-square test?

    <p>To compare observed and expected values</p> Signup and view all the answers

    How does the alternative hypothesis differ from the null hypothesis in a chi-square test?

    <p>It asserts a real difference between groups</p> Signup and view all the answers

    What is the formula used to calculate chi square?

    <p>Σ [ (Oi - Ei)2 / Ei ]</p> Signup and view all the answers

    What do the sum of the expected numbers and the sum of the observed numbers have in common?

    <p>They are equal</p> Signup and view all the answers

    What would be the calculated degrees of freedom for a table with 3 rows and 4 columns?

    <p>6</p> Signup and view all the answers

    What happens to the sum of the differences between observed and expected numbers?

    <p>It always comes to zero</p> Signup and view all the answers

    How are the differences between samples A and B related?

    <p>Each difference in A matches the same figure but with the opposite sign in B</p> Signup and view all the answers

    What is the reason for not rejecting the null hypothesis in the text?

    <p>Calculated χ2 value &lt; Tabulated χ2 value</p> Signup and view all the answers

    What type of variables is the chi-square statistic most appropriate for?

    <p>Categorical variables</p> Signup and view all the answers

    What type of data is used in the computation of the chi-square test statistic?

    <p>Frequency data</p> Signup and view all the answers

    What are the two sets of frequencies in chi-square analysis?

    <p>Observed and calculated frequencies</p> Signup and view all the answers

    If a data sample is sorted into a 2x2 contingency table based on two factors with two levels each, what is the total number of cells in the table?

    <p>4</p> Signup and view all the answers

    What does the expected number of observations for each cell represent in chi-square testing?

    <p>Hypothesized values under the null hypothesis</p> Signup and view all the answers

    What value is calculated in chi-square testing to determine the relationship between two categorical variables?

    <p>Chi-square test statistic</p> Signup and view all the answers

    What is the main purpose of the Chi-Square goodness of fit test?

    <p>To determine if sample data align with a hypothesized distribution</p> Signup and view all the answers

    How is the Chi-Square test statistic denoted?

    <p>Χ²</p> Signup and view all the answers

    What does the null hypothesis (Ho) state in a Chi-Square goodness of fit test?

    <p>The data align with a specified distribution</p> Signup and view all the answers

    What is the significance level used for in a Chi-Square goodness of fit test?

    <p>To establish the cutoff point for acceptance/rejection of the null hypothesis</p> Signup and view all the answers

    What formula is used to calculate the test statistic chi-square random variable (Χ2)?

    <p>Χ2 = Σ [ (Oi - Ei)2 / Ei ]</p> Signup and view all the answers

    When is the Chi-Square goodness of fit test used?

    <p>To assess whether data align with a hypothesized distribution</p> Signup and view all the answers

    When comparing the P-value to the significance level, what action is taken if the P-value is less than the significance level?

    <p>Reject the null hypothesis</p> Signup and view all the answers

    What does the alternative hypothesis (Ha) state in a Chi-Square goodness of fit test?

    <p>The data do not align with a specified distribution</p> Signup and view all the answers

    In which situation is the chi-square goodness of fit test appropriate?

    <p>When the expected value of the number of sample observations in each level is at least 5</p> Signup and view all the answers

    How is the expected number of observations (E) calculated for each level?

    <p>Ei = npi</p> Signup and view all the answers

    What does the chi-square test statistic represent?

    <p>A measure of the discrepancy between observed and expected values</p> Signup and view all the answers

    For what purpose can the chi-square distribution be used?

    <p>Testing hypotheses when the data are in the form of frequencies</p> Signup and view all the answers

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