Question

How do you find the margin of error from the lower and upper bounds of a...

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]

Homework Answers

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.

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