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