Question

How do you find the margin of error from the lower and upper bounds of a confidence interval? [1 sentence]

What is the effect of increasing the standard deviation on the margin of error? [2 sentences]

Why does increasing the confidence level result in a larger margin of error? [2 sentences]

Why would you be more likely to use a T-interval in a real-world situation than a Z-interval? [2 sentences]

When do you use the t-distribution to determine the confidence interval for the mean? [3 sentences]

Answer 1

a) The margin of error could be computed form the Lower bound, L and upper bound U as:

b) The margin of error is computed as:

Therefore the margin of error increases with standard deviation.

c) A larger confidence level results into a larger critical z value z* and as we saw in previous part that margin of error is directly proportional to the critical value, therefore increasing confidence level increases the margin of error.

d) In a real world situation, when the distribution is not normal and t distribution is used, also when the extreme events are more likely, the t distribution better represents the distributions and therefore T - interval is more useful in the real world situation than a Z interval.

e) The t distribution is used to compute the confidence interval of mean when the underlying distribution is not given to be normal.