AP Statistics Flashcards: Chi Square Goodness Of Fit Test

What this deck covers

This deck focuses on Chi Square Goodness Of Fit Test, giving you a quick way to review the definitions, rules, and examples that matter most for AP Statistics.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the consequence if expected frequencies are less than 5?

Answer: Chi-Square test may not be valid. Violates assumptions needed for valid statistical inference.

Flashcard 2: What is the standard level of significance used in hypothesis testing?

Answer: 0.05. Most commonly used threshold for statistical significance.

Flashcard 3: Identify the primary condition for using the Chi-Square test.

Answer: Data must be categorical. Chi-square tests require frequency counts of categories.

Flashcard 4: What is the critical value in a Chi-Square test used for?

Answer: To determine whether to reject the null hypothesis. Compare with test statistic to make statistical decision.

Flashcard 5: What is the primary goal of calculating the expected frequencies?

Answer: To compare against observed frequencies. Baseline for measuring deviation from null hypothesis.

Flashcard 6: Identify the primary condition for using the Chi-Square test.

Answer: Data must be categorical. Chi-square tests require frequency counts of categories.

Flashcard 7: What happens to the Chi-Square distribution as degrees of freedom increase?

Answer: It becomes more symmetric. Approaches normal distribution as degrees of freedom increase.

Flashcard 8: What is the effect of increasing the sample size on the Chi-Square test?

Answer: Increases the power of the test. Larger samples better detect true differences from null.

Flashcard 9: Choose the appropriate test: 'Comparing the distribution of a sample to a theoretical distribution.'

Answer: Chi-Square Goodness of Fit test. Tests if sample matches theoretical distribution pattern.

Flashcard 10: Which type of data is inappropriate for a Chi-Square test?

Answer: Continuous data. Chi-square requires categorical frequency data only.

Flashcard 11: Find the degrees of freedom for a test with 7 categories.

Answer: Degrees of freedom = 6. Formula: $df = k - 1$ where $k$ is categories.

Flashcard 12: Choose the appropriate test: 'Comparing the distribution of a sample to a theoretical distribution.'

Answer: Chi-Square Goodness of Fit test. Tests if sample matches theoretical distribution pattern.

Flashcard 13: What criterion determines the rejection of the null hypothesis in a Chi-Square test?

Answer: Chi-Square statistic > critical value. Decision rule for hypothesis testing with chi-square.

Flashcard 14: What is the effect of increasing the sample size on the Chi-Square test?

Answer: Increases the power of the test. Larger samples better detect true differences from null.

Flashcard 15: Identify the degrees of freedom for a Chi-Square Goodness of Fit test with 5 categories.

Answer: Degrees of freedom = 4. Formula: $df = k - 1$ where $k$ is number of categories.

Flashcard 16: What is the relationship between Chi-Square statistic and p-value?

Answer: Higher Chi-Square statistic typically results in a lower p-value. Larger deviations produce higher statistics and lower p-values.

Flashcard 17: What is the assumption about the expected frequency in a Chi-Square test?

Answer: Expected frequency should be at least 5. Ensures valid approximation to chi-square distribution.

Flashcard 18: What does a p-value greater than 0.05 suggest in a Chi-Square test?

Answer: Fail to reject the null hypothesis. Insufficient evidence to reject null hypothesis.

Flashcard 19: Identify the assumption about sample size in a Chi-Square test.

Answer: Sample size should be large enough to ensure expected frequencies are at least 5. Prevents invalid approximation to chi-square distribution.

Flashcard 20: What is the relationship between Chi-Square statistic and p-value?

Answer: Higher Chi-Square statistic typically results in a lower p-value. Larger deviations produce higher statistics and lower p-values.

Flashcard 21: What is the purpose of a Chi-Square Test for Goodness of Fit?

Answer: To determine if observed frequencies match expected frequencies. Tests if data follows a specific distribution pattern.

Flashcard 22: What are the two main types of Chi-Square tests?

Answer: Goodness of Fit and Test of Independence. Both test distribution assumptions but in different ways.

Flashcard 23: Which hypothesis do you reject if the Chi-Square statistic exceeds the critical value?

Answer: Null hypothesis. Reject when evidence strongly contradicts null assumption.

Flashcard 24: Identify the correct statement: 'Chi-Square test is for categorical or numerical data?'

Answer: Categorical data. Chi-square applies to frequency counts of categories.

Flashcard 25: What is the critical value in a Chi-Square test used for?

Answer: To determine whether to reject the null hypothesis. Compare with test statistic to make statistical decision.

Flashcard 26: Identify the effect of a larger Chi-Square statistic value.

Answer: Greater evidence against the null hypothesis. Higher values indicate greater deviation from expected.

Flashcard 27: Identify the assumption about sample size in a Chi-Square test.

Answer: Sample size should be large enough to ensure expected frequencies are at least 5. Prevents invalid approximation to chi-square distribution.

Flashcard 28: Identify the degrees of freedom for a Chi-Square Goodness of Fit test with 5 categories.

Answer: Degrees of freedom = 4. Formula: $df = k - 1$ where $k$ is number of categories.

Flashcard 29: Which type of data is inappropriate for a Chi-Square test?

Answer: Continuous data. Chi-square requires categorical frequency data only.

Flashcard 30: What is the formula for calculating degrees of freedom in a Chi-Square Goodness of Fit test?

Answer: $df = k - 1$. Where $k$ is the number of categories being tested.

Flashcard 31: What is the primary goal of calculating the expected frequencies?

Answer: To compare against observed frequencies. Baseline for measuring deviation from null hypothesis.

Flashcard 32: What is the null hypothesis in a Chi-Square Goodness of Fit test?

Answer: The observed frequencies match the expected frequencies. Assumes the theoretical distribution is correct.

Flashcard 33: How do you calculate expected frequency for each category?

Answer: $E_i = \frac{\text{Total Observed} \times \text{Proportion}}{1}$. Multiply total sample size by theoretical probability.

Flashcard 34: Find the degrees of freedom for a test with 10 categories.

Answer: Degrees of freedom = 9. Formula: $df = k - 1$ where $k$ is categories.

Flashcard 35: What is the consequence if expected frequencies are less than 5?

Answer: Chi-Square test may not be valid. Violates assumptions needed for valid statistical inference.

Flashcard 36: What is the formula for calculating degrees of freedom in a Chi-Square Goodness of Fit test?

Answer: $df = k - 1$. Where $k$ is the number of categories being tested.

Flashcard 37: Which distribution is used for the Chi-Square test?

Answer: Chi-Square distribution. Theoretical distribution for chi-square test statistic.

Flashcard 38: How do you calculate expected frequency for each category?

Answer: $E_i = \frac{\text{Total Observed} \times \text{Proportion}}{1}$. Multiply total sample size by theoretical probability.

Flashcard 39: What is the null hypothesis in a Chi-Square Goodness of Fit test?

Answer: The observed frequencies match the expected frequencies. Assumes the theoretical distribution is correct.

Flashcard 40: Find the critical value for a Chi-Square test with 3 degrees of freedom at 0.05 significance.

Answer: 7.815. From chi-square table with $\alpha = 0.05$ and $df = 3$.

Flashcard 41: What does a p-value greater than 0.05 suggest in a Chi-Square test?

Answer: Fail to reject the null hypothesis. Insufficient evidence to reject null hypothesis.

Flashcard 42: What is the shape of the Chi-Square distribution?

Answer: Right-skewed. Chi-square values are always non-negative with long right tail.

Flashcard 43: What does a low p-value indicate in a Chi-Square test?

Answer: Strong evidence against the null hypothesis. Small p-values suggest data unlikely under null hypothesis.

Flashcard 44: Find the degrees of freedom for a test with 7 categories.

Answer: Degrees of freedom = 6. Formula: $df = k - 1$ where $k$ is categories.

Flashcard 45: What does $E_i$ represent in the Chi-Square formula?

Answer: $E_i$ represents the expected frequency. The subscript $i$ denotes each category under null hypothesis.

Flashcard 46: What is the purpose of a Chi-Square Test for Goodness of Fit?

Answer: To determine if observed frequencies match expected frequencies. Tests if data follows a specific distribution pattern.

Flashcard 47: State the formula for the Chi-Square statistic.

Answer: $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$. Compares observed and expected frequencies for each category.

Flashcard 48: Which distribution is used for the Chi-Square test?

Answer: Chi-Square distribution. Theoretical distribution for chi-square test statistic.

Flashcard 49: What is the significance level commonly used in a Chi-Square test?

Answer: 0.05. Standard alpha level for hypothesis testing.

Flashcard 50: Which table do you use to find Chi-Square critical values?

Answer: Chi-Square distribution table. Provides critical values based on degrees of freedom.

Flashcard 51: What does $E_i$ represent in the Chi-Square formula?

Answer: $E_i$ represents the expected frequency. The subscript $i$ denotes each category under null hypothesis.

Flashcard 52: What does a significant Chi-Square result indicate?

Answer: Observed frequencies differ from expected frequencies. Provides evidence against null hypothesis of equal distribution.

Flashcard 53: What happens to the Chi-Square distribution as degrees of freedom increase?

Answer: It becomes more symmetric. Approaches normal distribution as degrees of freedom increase.

Flashcard 54: Find the critical value for a Chi-Square test with 3 degrees of freedom at 0.05 significance.

Answer: 7.815. From chi-square table with $\alpha = 0.05$ and $df = 3$.

Flashcard 55: What does a low p-value indicate in a Chi-Square test?

Answer: Strong evidence against the null hypothesis. Small p-values suggest data unlikely under null hypothesis.

Flashcard 56: Find the degrees of freedom for a test with 10 categories.

Answer: Degrees of freedom = 9. Formula: $df = k - 1$ where $k$ is categories.

Flashcard 57: How is the p-value related to the Chi-Square statistic?

Answer: P-value indicates the probability of observing a test statistic as extreme. Area under chi-square curve beyond observed statistic.

Flashcard 58: Identify the correct statement: 'Chi-Square test is for categorical or numerical data?'

Answer: Categorical data. Chi-square applies to frequency counts of categories.

Flashcard 59: What are the two main types of Chi-Square tests?

Answer: Goodness of Fit and Test of Independence. Both test distribution assumptions but in different ways.

Flashcard 60: What is the assumption about the expected frequency in a Chi-Square test?

Answer: Expected frequency should be at least 5. Ensures valid approximation to chi-square distribution.

Flashcard 61: How is the p-value related to the Chi-Square statistic?

Answer: P-value indicates the probability of observing a test statistic as extreme. Area under chi-square curve beyond observed statistic.

Flashcard 62: What is the alternative hypothesis in a Chi-Square Goodness of Fit test?

Answer: The observed frequencies do not match the expected frequencies. At least one category differs from expected distribution.

Flashcard 63: What does $O_i$ represent in the Chi-Square formula?

Answer: $O_i$ represents the observed frequency. The subscript $i$ denotes each category in the data set.

Flashcard 64: What is the alternative hypothesis in a Chi-Square Goodness of Fit test?

Answer: The observed frequencies do not match the expected frequencies. At least one category differs from expected distribution.

Flashcard 65: What is the standard level of significance used in hypothesis testing?

Answer: 0.05. Most commonly used threshold for statistical significance.

Flashcard 66: Which hypothesis do you reject if the Chi-Square statistic exceeds the critical value?

Answer: Null hypothesis. Reject when evidence strongly contradicts null assumption.

Flashcard 67: Which table do you use to find Chi-Square critical values?

Answer: Chi-Square distribution table. Provides critical values based on degrees of freedom.

Flashcard 68: What does $O_i$ represent in the Chi-Square formula?

Answer: $O_i$ represents the observed frequency. The subscript $i$ denotes each category in the data set.

Flashcard 69: What criterion determines the rejection of the null hypothesis in a Chi-Square test?

Answer: Chi-Square statistic > critical value. Decision rule for hypothesis testing with chi-square.

Flashcard 70: What is the significance level commonly used in a Chi-Square test?

Answer: 0.05. Standard alpha level for hypothesis testing.

Flashcard 71: What does a significant Chi-Square result indicate?

Answer: Observed frequencies differ from expected frequencies. Provides evidence against null hypothesis of equal distribution.

Flashcard 72: Identify the effect of a larger Chi-Square statistic value.

Answer: Greater evidence against the null hypothesis. Higher values indicate greater deviation from expected.