Final answer:
The margin of error and the level of significance are related in statistical hypothesis testing. As the level of significance decreases, the margin of error increases. The margin of error is also inversely related to the sample size.
Step-by-step explanation:
The margin of error and the level of significance are related in statistical hypothesis testing. The margin of error represents the range of values within which the true population parameter is likely to fall. The level of significance, often denoted as alpha (α), is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.
As the level of significance decreases (e.g., from 10% to 5% to 1%), the margin of error increases. This means that the range of acceptable values for the population parameter becomes wider, allowing for more uncertainty in the estimate. Conversely, as the level of significance increases, the margin of error decreases, resulting in a narrower range of acceptable values and a more precise estimate.
The margin of error is also inversely related to the sample size. As the sample size increases, the margin of error decreases. This is because larger samples provide more information and tend to better represent the population. With a larger sample size, the estimate becomes more precise, leading to a smaller margin of error.