# What are the assumptions for estimating a confidence interval through bootstrapping?

Context

I created a rule based classification model for flagging emails about a certain topic. The process for creating that model, was to look at contents and flagging the email if certain terms are used.

I now want to estimate the number of flagged emails for 2019. For this estimation we took 400 emails at random during 2019 and had the following results:

• True Positive: 40
• False Positive: 10
• True Negative: 300
• False Negative: 50

Method 1

The easiest way to estimate the volume of flagged emails for 2019 would be to use the proportion found on the sample:

• (40 + 50) / 400 = 0.225
• Confidence interval with N = 400, p = 0.225 and z = 1.96 --> +- 0.04

Imagine 100,000 emails in 2019, the estimate would be: 22,500 +- 896 flagged

Method 2

I was thinking I could use the model to be more accurate:

• Coefficient ratio (TP + FN) / (TP + FP) = 1.8
• Bootstrap 1000 times with a resample of 400 emails and 95% confidence : +- 0.06 (fictional number)

Imagine 12,000 of the 100,000 emails tagged by the model in 2019, the estimate would be: 21,600 +- 720

Questions

• Can I apply method 2 ? Or have I missed an essential assumption?

• Which method would be most appropriate for estimating the number of flagged emails in 2019?