At MacroPulse, a financial intelligence platform, analysts publish a weekly “global outlook” note. Management wants to know whether the team’s briefing process is actually aligned with real global economic movement, rather than just reacting to noise.
You are given 12 recent months of data comparing the platform’s monthly economic sentiment score with the actual monthly global GDP growth surprise index. Test whether the average difference between the two series is zero, and quantify the uncertainty around that difference.
The sentiment score and GDP surprise index are both standardized to comparable monthly units.
| Month | Sentiment Score | GDP Surprise Index | Difference (Sentiment - GDP) |
|---|---|---|---|
| 1 | 0.42 | 0.35 | 0.07 |
| 2 | 0.31 | 0.28 | 0.03 |
| 3 | 0.15 | 0.22 | -0.07 |
| 4 | -0.05 | 0.01 | -0.06 |
| 5 | -0.18 | -0.12 | -0.06 |
| 6 | -0.12 | -0.08 | -0.04 |
| 7 | 0.08 | 0.02 | 0.06 |
| 8 | 0.21 | 0.17 | 0.04 |
| 9 | 0.27 | 0.19 | 0.08 |
| 10 | 0.11 | 0.09 | 0.02 |
| 11 | -0.09 | -0.03 | -0.06 |
| 12 | 0.05 | 0.01 | 0.04 |
Use a significance level of 0.05.