To determine the expected frequencies, we use the formula for each cell in a contingency table:

$\text{Expected frequency} = \frac{(\text{Row total} \times \text{Column total})}{\text{Grand total}}$

Given the data provided, here is a breakdown of the steps:

1. Grand Total = 200
2. Status regarding lab techniques course totals:
   • Took the course: 73
   • Didn’t take the course: 127
3. Laboratory performance totals:
   • No incidents: 103
   • Exactly one incident: 63
   • 2+ incidents: 34

Calculating the Missing Expected Frequencies

1. For "Took the course" and "Involved in exactly one incident":

$\text{Expected frequency} = \frac{(73 \times 63)}{200} = 23.03$

2. For "Took the course" and "Involved in 2+ incidents":

$\text{Expected frequency} = \frac{(73 \times 34)}{200} = 12.41$

3. For "Didn't take the course" and "Involved in no incident":

$\text{Expected frequency} = \frac{(127 \times 103)}{200} = 65.42$

Completed Contingency Table with Expected Frequencies

Let me know if you want a detailed explanation of the calculations or if you have any questions!

Related Questions

1. How can we test if the variables are independent using this table?
2. What would the chi-square value be for this contingency table?
3. Why is it important to check for independence in this data?
4. What does a high chi-square value indicate in this context?
5. How would the results differ if the totals for each category changed?

Tip: When calculating expected values, always ensure the row and column totals match to verify calculations.