AP Statistics Flashcards: Expected Counts In Two Way Tables

What this deck covers

This deck focuses on Expected Counts In Two Way Tables, 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 expected count if Row Total = 55, Column Total = 25, and Grand Total = 250?

Answer: Expected Count = 5.5. Calculate: $\frac{55 \times 25}{250} = \frac{1375}{250} = 5.5$

Flashcard 2: Find the expected count: Row Total = 45, Column Total = 15, Grand Total = 90.

Answer: Expected Count = 7.5. Calculate: $\frac{45 \times 15}{90} = \frac{675}{90} = 7.5$

Flashcard 3: Which condition must be met for expected counts in a chi-square test?

Answer: Each expected count should be at least 5. This ensures the chi-square distribution approximation is valid for the test.

Flashcard 4: Calculate the expected count for a cell: Row Total = 45, Column Total = 15, Grand Total = 135.

Answer: Expected Count = 5. Calculate: $\frac{45 \times 15}{135} = \frac{675}{135} = 5$

Flashcard 5: Identify the formula to compute the expected count for a cell in a contingency table.

Answer: Expected Count = $\frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}$. Standard formula for expected frequencies in contingency tables under independence assumption.

Flashcard 6: What expected count results from Row Total = 25, Column Total = 40, Grand Total = 200?

Answer: Expected Count = 5. Calculate: $\frac{25 \times 40}{200} = \frac{1000}{200} = 5$

Flashcard 7: Find the expected count: Row Total = 30, Column Total = 60, Grand Total = 180.

Answer: Expected Count = 10. Calculate: $\frac{30 \times 60}{180} = \frac{1800}{180} = 10$

Flashcard 8: What is the expected count if Row Total = 60, Column Total = 20, and Grand Total = 240?

Answer: Expected Count = 5. Calculate: $\frac{60 \times 20}{240} = \frac{1200}{240} = 5$

Flashcard 9: How do observed counts relate to expected counts in hypothesis testing?

Answer: Observed counts are compared to expected counts to test independence. Large differences between observed and expected suggest dependence between variables.

Flashcard 10: What conclusion is drawn if observed counts significantly differ from expected counts?

Answer: There may be an association between the variables. Significant differences suggest the variables are not independent of each other.

Flashcard 11: If a table's row total is 25 and column total is 10 with grand total 100, what is the expected count?

Answer: Expected Count = 2.5. Calculate: $\frac{25 \times 10}{100} = \frac{250}{100} = 2.5$

Flashcard 12: What expected count results from Row Total = 36, Column Total = 12, Grand Total = 300?

Answer: Expected Count = 1.44. Calculate: $\frac{36 \times 12}{300} = \frac{432}{300} = 1.44$

Flashcard 13: What does it mean if expected counts match observed counts?

Answer: It suggests that the variables are likely independent. Close agreement indicates no significant association between the categorical variables.

Flashcard 14: Which values are needed to calculate expected counts in a two-way table?

Answer: Row Total, Column Total, Grand Total. These three marginal totals are required components for the expected count formula.

Flashcard 15: Identify the formula to compute the expected count for a cell in a contingency table.

Answer: Expected Count = $\frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}$. Standard formula for expected frequencies in contingency tables under independence assumption.

Flashcard 16: What is the expected count for a cell with Row Total = 100, Column Total = 25, Grand Total = 1000?

Answer: Expected Count = 2.5. Calculate: $\frac{100 \times 25}{1000} = \frac{2500}{1000} = 2.5$

Flashcard 17: What is the expected count if Row Total = 60, Column Total = 20, and Grand Total = 240?

Answer: Expected Count = 5. Calculate: $\frac{60 \times 20}{240} = \frac{1200}{240} = 5$

Flashcard 18: Which condition must be met for expected counts in a chi-square test?

Answer: Each expected count should be at least 5. This ensures the chi-square distribution approximation is valid for the test.

Flashcard 19: How do you calculate the expected count for a cell in a two-way table?

Answer: Use Expected Count = $\frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}$. Apply this formula to find theoretical frequency for any cell in a two-way table.

Flashcard 20: What conclusion is drawn if observed counts significantly differ from expected counts?

Answer: There may be an association between the variables. Significant differences suggest the variables are not independent of each other.

Flashcard 21: What is the expected count for a cell with Row Total = 100, Column Total = 25, Grand Total = 1000?

Answer: Expected Count = 2.5. Calculate: $\frac{100 \times 25}{1000} = \frac{2500}{1000} = 2.5$

Flashcard 22: What expected count results from Row Total = 25, Column Total = 40, Grand Total = 200?

Answer: Expected Count = 5. Calculate: $\frac{25 \times 40}{200} = \frac{1000}{200} = 5$

Flashcard 23: Calculate the expected count for a cell: Row Total = 75, Column Total = 50, Grand Total = 300.

Answer: Expected Count = 12.5. Calculate: $\frac{75 \times 50}{300} = \frac{3750}{300} = 12.5$

Flashcard 24: Calculate the expected count for a cell with Row Total = 50 and Column Total = 30 in a 150 total table.

Answer: Expected Count = 10. Calculate: $\frac{50 \times 30}{150} = \frac{1500}{150} = 10$

Flashcard 25: If a table's row total is 25 and column total is 10 with grand total 100, what is the expected count?

Answer: Expected Count = 2.5. Calculate: $\frac{25 \times 10}{100} = \frac{250}{100} = 2.5$

Flashcard 26: Calculate the expected count for a cell with Row Total = 50 and Column Total = 30 in a 150 total table.

Answer: Expected Count = 10. Calculate: $\frac{50 \times 30}{150} = \frac{1500}{150} = 10$

Flashcard 27: If a table's row total is 90 and column total is 40 with grand total 360, what is the expected count?

Answer: Expected Count = 10. Calculate: $\frac{90 \times 40}{360} = \frac{3600}{360} = 10$

Flashcard 28: What is the expected count if Row Total is 40, Column Total is 50, and Grand Total is 200?

Answer: Expected Count = 10. Calculate: $\frac{40 \times 50}{200} = \frac{2000}{200} = 10$

Flashcard 29: How do you calculate the expected count for a cell in a two-way table?

Answer: Use Expected Count = $\frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}$. Apply this formula to find theoretical frequency for any cell in a two-way table.

Flashcard 30: Find the expected count: Row Total = 90, Column Total = 10, Grand Total = 300.

Answer: Expected Count = 3. Calculate: $\frac{90 \times 10}{300} = \frac{900}{300} = 3$

Flashcard 31: What is the expected count for a cell with Row Total = 50, Column Total = 100, Grand Total = 1000?

Answer: Expected Count = 5. Calculate: $\frac{50 \times 100}{1000} = \frac{5000}{1000} = 5$

Flashcard 32: What result would indicate no association between variables in a two-way table?

Answer: Observed counts are close to expected counts. Similar observed and expected counts suggest the variables are independent.

Flashcard 33: What expected count results from Row Total = 80, Column Total = 20, Grand Total = 1600?

Answer: Expected Count = 1. Calculate: $\frac{80 \times 20}{1600} = \frac{1600}{1600} = 1$

Flashcard 34: Identify the effect of increasing sample size on expected counts.

Answer: Larger sample sizes generally increase expected counts. More data points increase the marginal totals, which typically increases expected frequencies.

Flashcard 35: Find the expected count: Row Total = 60, Column Total = 30, Grand Total = 600.

Answer: Expected Count = 3. Calculate: $\frac{60 \times 30}{600} = \frac{1800}{600} = 3$

Flashcard 36: Calculate the expected count for a cell: Row Total = 45, Column Total = 15, Grand Total = 135.

Answer: Expected Count = 5. Calculate: $\frac{45 \times 15}{135} = \frac{675}{135} = 5$

Flashcard 37: What does a high chi-square statistic indicate about expected vs. observed counts?

Answer: A high chi-square suggests a significant difference between observed and expected counts. Large chi-square values indicate substantial deviation from independence assumption.

Flashcard 38: What is the expected count if Row Total is 40, Column Total is 50, and Grand Total is 200?

Answer: Expected Count = 10. Calculate: $\frac{40 \times 50}{200} = \frac{2000}{200} = 10$

Flashcard 39: Determine the expected count for a cell with Row Total = 70, Column Total = 45, Grand Total = 315.

Answer: Expected Count = 10. Calculate: $\frac{70 \times 45}{315} = \frac{3150}{315} = 10$

Flashcard 40: How are expected counts used in determining statistical significance?

Answer: They are compared with observed counts to compute the chi-square statistic. The chi-square statistic measures how much observed counts deviate from expected counts.

Flashcard 41: What is the expected count for a cell with Row Total = 50, Column Total = 100, Grand Total = 1000?

Answer: Expected Count = 5. Calculate: $\frac{50 \times 100}{1000} = \frac{5000}{1000} = 5$

Flashcard 42: Find the expected count: Row Total = 50, Column Total = 50, Grand Total = 500.

Answer: Expected Count = 5. Calculate: $\frac{50 \times 50}{500} = \frac{2500}{500} = 5$

Flashcard 43: How do observed counts relate to expected counts in hypothesis testing?

Answer: Observed counts are compared to expected counts to test independence. Large differences between observed and expected suggest dependence between variables.

Flashcard 44: What is the interpretation of an expected count in a two-way table?

Answer: The expected count is the theoretical frequency of a cell if there's no association. Represents what the cell frequency would be if the variables were independent.

Flashcard 45: Find the expected count: Row Total = 60, Column Total = 30, Grand Total = 600.

Answer: Expected Count = 3. Calculate: $\frac{60 \times 30}{600} = \frac{1800}{600} = 3$

Flashcard 46: Find the expected count: Row Total = 50, Column Total = 50, Grand Total = 500.

Answer: Expected Count = 5. Calculate: $\frac{50 \times 50}{500} = \frac{2500}{500} = 5$

Flashcard 47: In which situation would you use expected counts in a two-way table?

Answer: To test the independence of two categorical variables. Expected counts help determine if categorical variables are independent or associated.

Flashcard 48: What is the formula for expected count in a two-way table cell?

Answer: Expected Count = $\frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}$. This formula calculates theoretical frequency assuming independence between row and column variables.

Flashcard 49: What is the expected count for a cell with Row Total = 80, Column Total = 20, Grand Total = 200?

Answer: Expected Count = 8. Calculate: $\frac{80 \times 20}{200} = \frac{1600}{200} = 8$

Flashcard 50: What expected count results from Row Total = 36, Column Total = 12, Grand Total = 300?

Answer: Expected Count = 1.44. Calculate: $\frac{36 \times 12}{300} = \frac{432}{300} = 1.44$

Flashcard 51: What expected count results from Row Total = 80, Column Total = 20, Grand Total = 1600?

Answer: Expected Count = 1. Calculate: $\frac{80 \times 20}{1600} = \frac{1600}{1600} = 1$

Flashcard 52: What is the expected count if Row Total = 55, Column Total = 25, and Grand Total = 250?

Answer: Expected Count = 5.5. Calculate: $\frac{55 \times 25}{250} = \frac{1375}{250} = 5.5$

Flashcard 53: Find the expected count: Row Total = 120, Column Total = 40, Grand Total = 240.

Answer: Expected Count = 20. Calculate: $\frac{120 \times 40}{240} = \frac{4800}{240} = 20$

Flashcard 54: What is the interpretation of an expected count in a two-way table?

Answer: The expected count is the theoretical frequency of a cell if there's no association. Represents what the cell frequency would be if the variables were independent.

Flashcard 55: Determine the expected count for a cell with Row Total = 35, Column Total = 35, Grand Total = 245.

Answer: Expected Count = 5. Calculate: $\frac{35 \times 35}{245} = \frac{1225}{245} = 5$

Flashcard 56: What does a high chi-square statistic indicate about expected vs. observed counts?

Answer: A high chi-square suggests a significant difference between observed and expected counts. Large chi-square values indicate substantial deviation from independence assumption.

Flashcard 57: Which statistical test utilizes expected counts in a two-way table?

Answer: Chi-square test of independence. This test compares observed frequencies to expected frequencies to assess independence.

Flashcard 58: If a table's row total is 100 and column total is 25 with grand total 500, what is the expected count?

Answer: Expected Count = 5. Calculate: $\frac{100 \times 25}{500} = \frac{2500}{500} = 5$

Flashcard 59: If a table's row total is 90 and column total is 40 with grand total 360, what is the expected count?

Answer: Expected Count = 10. Calculate: $\frac{90 \times 40}{360} = \frac{3600}{360} = 10$

Flashcard 60: If a table's row total is 100 and column total is 25 with grand total 500, what is the expected count?

Answer: Expected Count = 5. Calculate: $\frac{100 \times 25}{500} = \frac{2500}{500} = 5$

Flashcard 61: What result would indicate no association between variables in a two-way table?

Answer: Observed counts are close to expected counts. Similar observed and expected counts suggest the variables are independent.

Flashcard 62: Which statistical test utilizes expected counts in a two-way table?

Answer: Chi-square test of independence. This test compares observed frequencies to expected frequencies to assess independence.

Flashcard 63: Which values are needed to calculate expected counts in a two-way table?

Answer: Row Total, Column Total, Grand Total. These three marginal totals are required components for the expected count formula.

Flashcard 64: Determine the expected count for a cell with Row Total = 35, Column Total = 35, Grand Total = 245.

Answer: Expected Count = 5. Calculate: $\frac{35 \times 35}{245} = \frac{1225}{245} = 5$

Flashcard 65: Determine the expected count for a cell with Row Total = 70, Column Total = 45, Grand Total = 315.

Answer: Expected Count = 10. Calculate: $\frac{70 \times 45}{315} = \frac{3150}{315} = 10$

Flashcard 66: What is the expected count for a cell with Row Total = 80, Column Total = 20, Grand Total = 200?

Answer: Expected Count = 8. Calculate: $\frac{80 \times 20}{200} = \frac{1600}{200} = 8$

Flashcard 67: Calculate the expected count for a cell: Row Total = 75, Column Total = 50, Grand Total = 300.

Answer: Expected Count = 12.5. Calculate: $\frac{75 \times 50}{300} = \frac{3750}{300} = 12.5$

Flashcard 68: What does it mean if expected counts match observed counts?

Answer: It suggests that the variables are likely independent. Close agreement indicates no significant association between the categorical variables.

Flashcard 69: Find the expected count: Row Total = 30, Column Total = 60, Grand Total = 180.

Answer: Expected Count = 10. Calculate: $\frac{30 \times 60}{180} = \frac{1800}{180} = 10$

Flashcard 70: What is the formula for expected count in a two-way table cell?

Answer: Expected Count = $\frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}$. This formula calculates theoretical frequency assuming independence between row and column variables.

Flashcard 71: In which situation would you use expected counts in a two-way table?

Answer: To test the independence of two categorical variables. Expected counts help determine if categorical variables are independent or associated.

Flashcard 72: Find the expected count: Row Total = 90, Column Total = 10, Grand Total = 300.

Answer: Expected Count = 3. Calculate: $\frac{90 \times 10}{300} = \frac{900}{300} = 3$

Flashcard 73: Identify the effect of increasing sample size on expected counts.

Answer: Larger sample sizes generally increase expected counts. More data points increase the marginal totals, which typically increases expected frequencies.

Flashcard 74: How are expected counts used in determining statistical significance?

Answer: They are compared with observed counts to compute the chi-square statistic. The chi-square statistic measures how much observed counts deviate from expected counts.

Flashcard 75: Find the expected count: Row Total = 45, Column Total = 15, Grand Total = 90.

Answer: Expected Count = 7.5. Calculate: $\frac{45 \times 15}{90} = \frac{675}{90} = 7.5$