1. To find the margin of error from the lower and upper bounds of a confidence interval, subtract the lower bound from the upper bound and divide by 2.

2. Increasing the standard deviation increases the margin of error because the sample variability grows, leading to a wider confidence interval. This reflects greater uncertainty in the population parameter.

3. Increasing the confidence level results in a larger margin of error because a higher confidence level requires a wider interval to capture the true population parameter with more certainty.

4. In real-world situations, you are more likely to use a T-interval because it accounts for the additional uncertainty when the sample size is small or when the population standard deviation is unknown. The T-distribution is more flexible for smaller or less well-known datasets.

5. The t-distribution is used to determine the confidence interval for the mean when the sample size is small (usually n < 30) or when the population standard deviation is unknown. It compensates for the additional uncertainty due to the smaller sample size. As the sample size increases, the t-distribution approaches the normal distribution.

Would you like further details on any of these points?

Here are 5 related questions:

1. How does increasing the sample size affect the margin of error?
2. What is the formula for the margin of error in a Z-interval?
3. How does the shape of the t-distribution compare to the normal distribution?
4. How does the margin of error change with different confidence levels?
5. Why does the t-distribution have "fatter tails" than the normal distribution?

Tip: When using the t-distribution, the degrees of freedom (n-1) play a crucial role in determining the shape and spread of the distribution.