Let's go step by step to find the missing values $A$ and $B$ for the given tables.

1. Finding $A$:

In the "Observed count" table, the sum of students in the "True" row is given as 79. So, we can determine $A$ by subtracting the other known values from 79:

$A = 79 - (34 + 17 + 7) = 79 - 58 = 21$

Thus, $A = 21$.

2. Finding $B$:

In the "Expected count" table, we need to calculate $B$, the expected count for "False" in the "3 (22-24)" age group.

The formula for calculating the expected count in a contingency table is:

$E_{ij} = \frac{(\text{Row Total}_i) \times (\text{Column Total}_j)}{\text{Grand Total}}$

For the "False" row in the "22-24" column:

• Row total for "False" = 71
• Column total for "22-24" = 35
• Grand total = 150

So, the expected count $B$ is:

$B = \frac{71 \times 35}{150} = \frac{2485}{150} = 16.567$

Thus, $B = 16.567$ (rounded to 3 decimal places).

Final Answers:

1. $A = 21$
2. $B = 16.567$

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Would you like more details or have any questions about the calculations? Here are 5 related questions for further exploration:

1. How is the chi-squared statistic calculated using observed and expected values?
2. What does a high chi-squared value indicate in this context?
3. Can the degrees of freedom in this chi-squared test be calculated?
4. What assumptions are made when using the chi-squared test for independence?
5. How would the conclusion change if $A$ and $B$ were significantly different from the calculated values?

Tip: When working with contingency tables, always double-check that the row and column sums match the totals in order to avoid errors in calculations.