Question

The table below shows the average attendance of school events by the day of the week on which they are held.

Average Attendance at School Events


Thursday
Friday
School Play
300
x
Band Concert
184
250

Which values of x will indicate an association between the two variables in the two-way table? Select the three correct answers.
250
304
407
422
714

Answer 1

To determine which values of \( x \) indicate an association between the average attendance of school events on different days of the week, we need to compare the attendance figures.

From the table:

- School Play on Thursday = 300
- School Play on Friday = \( x \)
- Band Concert on Thursday = 184
- Band Concert on Friday = 250

To explore the association, let's examine how the attendance number differs:

1. **If \( x \) is less than 300**:
- The Friday attendance for School Play is less than Thursday's attendance (300), which might indicate a drop in attendance. This could suggest that fewer people are willing to attend on Friday compared to Thursday.

2. **If \( x = 300**:
- This suggests that attendance on Friday is the same as Thursday, indicating no difference between the days.

3. **If \( x > 300**:
- This indicates that Friday's attendance has surpassed Thursday’s, suggesting an increase in attendance for School Plays on Friday.

To establish an association with the Band Concert figures:
- Notice that Band Concert attendance follows a similar trend, where Thursday (184) is less than Friday (250). An association leads to a consideration of how both events correlate to days of the week.

Considering the above logic, we want values of \( x \) that create a notable pattern of attendance relative to the days.

The values given in the problem are:
- 250
- 304
- 407
- 422
- 714

To create a positive association:
- \( x = 304 \): 304 (Friday) is more than 300 (Thursday). This shows a potential increase.
- \( x = 407 \): Clearly more than 300, again indicating a potential increase.
- \( x = 422 \): This is also more than 300, indicating an increase.

### Conclusion:
The values of \( x \) that indicate an association between the two variables (School Play attendance on Thursday and Friday) are:
- **304**
- **407**
- **422**

Thus, those values suggest a positive attendance association compared to the attendance on Thursday.