Confidence Intervals

Question 1

a confidence interval establishes the ___ of your estimate of the true value and it tells you nothing about ____

Answer 1

a confidence interval establishes the precision of your estimate of the true value and it tells you nothing about accuracy

“based on this sample, I am 95% sure that the average American is between this height and that height”

if your sample was not drawn randomly from the population, your estimate will be inaccurate

Question 2

how do you interpret “the Z-score corresponding to a 95% confidence interval is +/- 1.96”?

Answer 2

If you sampled 49 people from this population 100 times and took the mean of each sample, you would expect 95 of those sample means to be within 1.96 standard errors of the true value

Question 3

what is the equation for standard error?

Answer 3

standard error = sample standard deviation/square root of sample size

Question 4

explain the steps of calculating the confidence interval

Answer 4

• calculate the standard error
• choose a confidence limit
• look up the Z-score for that level of confidence
• convert that Z-score into the same units the data were presented in

Question 5

a confidence interval will be narrower if the population is ____ or if the sample is ____

Answer 5

a confidence interval will be narrower if the population is less variable or if the sample is larger

Question 6

contrast standard deviation vs. standard error

Answer 6

• standard deviation measures the variability of individuals in a sample (or in a population)
• standard error measures the variability of samples in a population

Question 7

describe standard error and standard deviation

Answer 7