University Statistics Test Questions on Calculating Expected Frequencies

📚 Quick Study Guide

• 📊 Expected frequency represents the frequency we'd anticipate in a category if the variables were independent.
• 🧮 The formula to calculate expected frequency is: $E = \frac{(Row Total) \times (Column Total)}{Grand Total}$.
• 📝 Ensure that you understand contingency tables, as they are the basis for calculating expected frequencies.
• 💡 Expected frequencies are used in Chi-Square tests to determine if there's a statistically significant association between two categorical variables.
• 🔍 If any expected frequency is too small (typically less than 5), the Chi-Square test may not be accurate, and adjustments or alternative tests might be needed.

Practice Quiz

1. Question 1: In a contingency table, if the row total is 50, the column total is 40, and the grand total is 200, what is the expected frequency for that cell?
   1. A) 5
   2. B) 10
   3. C) 15
   4. D) 20
2. Question 2: What statistical test primarily uses expected frequencies to analyze categorical data?
   1. A) T-test
   2. B) ANOVA
   3. C) Chi-Square Test
   4. D) Regression Analysis
3. Question 3: In a 2x2 contingency table, if all observed frequencies are equal, what would you expect the expected frequencies to be?
   1. A) All equal
   2. B) All zero
   3. C) Varying significantly
   4. D) Cannot be determined
4. Question 4: Which of the following is NOT needed to calculate expected frequencies?
   1. A) Row Totals
   2. B) Column Totals
   3. C) Grand Total
   4. D) Observed Frequencies
5. Question 5: In a contingency table, if the row total is 60, the column total is 80, and the grand total is 240, what is the expected frequency?
   1. A) 10
   2. B) 15
   3. C) 20
   4. D) 25
6. Question 6: What should you do if you find that many of your expected frequencies are less than 5?
   1. A) Proceed with the Chi-Square test as is.
   2. B) Increase the sample size or combine categories.
   3. C) Use a T-test instead.
   4. D) Ignore the low expected frequencies.
7. Question 7: A researcher is studying the relationship between smoking and lung cancer. What type of data (variables) are used to calculate expected frequencies in this scenario?
   1. A) Continuous Variables
   2. B) Categorical Variables
   3. C) Ordinal Variables
   4. D) Ratio Variables