Why is there a direct relationship between sample size and expected error rate?
Expected error rate is the likelihood that there is an error in the population. As an auditor, you would make this judgement based on prior year audits, walkthrough procedures performed, or any other assessments that may indicate whether there is a low or high chance of an error in a population.
Expected error rate has a direct relationship with sample size. That means that if the expected error rate is high, then the auditor should increase the sample size. If the expected error rate is low, then the auditor should decrease the sample size.
What is an example of relationship between sample size and expected error rate?
Imagine yourself in Sonoma California, and you are the owner of a small little winery. The winery is expected to bottle at least 100 pinot noirs this year. As the winemaker, you must sample the wine and make sure that it is drinkable and that it has not gone bad, right? The winemaker must decide how many bottles of wine to sample to feel comfortable that customers will not end up with a bad bottle of wine.
If the winemaker has a LOW reason to believe that the wine would be bad, they would have a LOW expected error rate. In that case, they would likely test a LOWER amount.
If the winemaker has a HIGH reason to believe that the wine could be bad, then they would have a HIGH expected error rate. In that situation, the winemaker would test a HIGHER amount.
At the end of the day, the winemaker must make a judgement call on how many bottles of wine to test before concluding that the wine can be sold to customers and they will not end up with a bad bottle of wine!
You might also be interested in...

Will sample size increase if the population variability is higher than expected?
Yes, there is a direct relationship between sample size and population variability. Population variability is how similar or dissimilar items in a population are. If the population variability increases, then that means that the items in the population aren’t as similar as the auditor expected. This increases the level of risk, so the audit team […]

Will sample size increase or decrease if there is an increase in the tolerable misstatement?
There is an inverse relationship between sample size and tolerable misstatement, so the sample size would decrease if the tolerable misstatement increases.

Will sample size increase or decrease if the assessed level of risk is higher than expected?
If the assessed level of risk is higher than what the auditor originally determined in the planning phase, then the audit team should increase their sample size or choose a testing method that provides for higher quality evidence.