Question 1188763: P1: Neeve conducts a test to determine whether there is any correlation between a person's age and the number of hours they spend watching television per week. ge 8 42 17 81 45 14 39 42 31 40 28 24 || No. of 20 15 30 2 25 28 19 14 16 21 26 20 hours a Write down a table of ranks for this data. (3 marks) b Calculate Spearman's rank correlation. (2 marks) C Neeve concludes that your age affects how much TV per week you tend to watch. Using your calculations, comment on whether or not Neeve is correct. Suggest what conclusions you are able to make from your calculations. (3 marks)
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to analyze Neeve's data:
**a. Table of Ranks:**
First, we need to rank the ages and the number of TV hours separately. Rank 1 goes to the smallest value, and the highest rank goes to the largest value. If there are ties, we take the average of the ranks that would have been assigned.
| Age | Rank (Age) | TV Hours | Rank (TV) |
|---|---|---|---|
| 8 | 1 | 20 | 6.5 |
| 42 | 8.5 | 15 | 4 |
| 17 | 2 | 30 | 10 |
| 81 | 12 | 2 | 1 |
| 45 | 10 | 25 | 8 |
| 14 | 3 | 28 | 9 |
| 39 | 6 | 19 | 5 |
| 42 | 8.5 | 14 | 3 |
| 31 | 5 | 16 | 4.5 |
| 40 | 7 | 21 | 7 |
| 28 | 4 | 26 | 8.5 |
| 24 | 3 | 20 | 6.5 |
**b. Spearman's Rank Correlation:**
Spearman's rank correlation coefficient (rs) is calculated using the formula:
rs = 1 - (6 * Σd²) / (n * (n² - 1))
Where 'd' is the difference between the ranks for each pair, and 'n' is the number of pairs (12 in this case).
1. Calculate 'd' for each pair: (Rank Age - Rank TV)
2. Calculate d² for each pair.
3. Sum the d² values (Σd²). You should get approximately 111.5
4. Apply the formula:
rs = 1 - (6 * 111.5) / (12 * (12² - 1))
rs = 1 - (669) / (12 * 143)
rs = 1 - (669) / (1716)
rs ≈ 1 - 0.39
rs ≈ 0.61
**c. Neeve's Conclusion:**
Neeve concludes that age *affects* how much TV a person watches. This implies a causal relationship. However, correlation does *not* equal causation. While there's a moderately positive correlation (rs ≈ 0.61), this only suggests that as age *tends* to increase, the number of TV hours *tends* to decrease. It does *not* prove that age *causes* a decrease in TV watching.
**Better Conclusions:**
* There is a moderate positive correlation between age and the number of hours spent watching television.
* Older individuals in this sample tend to watch less television than younger individuals.
* Other factors besides age could be influencing television viewing habits (e.g., lifestyle, work schedules, access to streaming services, etc.). Further investigation is needed to explore these potential influences. A larger sample size would also be beneficial.
Therefore, Neeve's conclusion is too strong. The data only supports a correlation, not a causal link.
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