Confidence intervals worksheet with answers

Free printable Confidence intervals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
n = 80, σ = 5LUx̄ = 156E = ?99%

A sample of 80 measurements has mean 156. The population standard deviation is known to be 5. Find the margin of error E of a 99% confidence interval for the mean.

n = 80x̄ = 156σ = 599%
E =
2.Easy
46.35x̄49.6590%

A 90% confidence interval for a mean, computed from 144 observations with a known population standard deviation, is [46.35, 49.65]. What standard deviation σ was used?

[46.35, 49.65]n = 14490%
σ =
3.Medium
n = 15, sd​ = 1.20LUd̄ = 7.9E = ?95%

The blood pressure of 15 patients is measured before and after a treatment. The differences d = before − after (mmHg) have mean 7.9 and standard deviation 1.2. Find the margin of error E of the 95% confidence interval for the mean difference.

n = 15d̄ = 7.9sd = 1.295%t(14) = 2.145
E = mmHg
4.Medium
n = 11, s = 5.5L = ?Ux̄ = 59E95%

A sample of 11 items has mean 59 and standard deviation s = 5.5. The population is roughly normal. Find the lower limit of the 95% confidence interval for the mean.

n = 11x̄ = 59s = 5.595%t(10) = 2.228
lower limit =
5.Hard
σ = 31, n = ?x̄ − Ex̄ + Ex̄E = 190%

The population standard deviation is 31. How large a sample n do you need so that a 90% confidence interval for the mean has a margin of error of at most 1?

σ = 31E = 190%
n =
6.Hard
σ = 27, n = ?x̄ − Ex̄ + Ex̄E = 1.599%

The population standard deviation is 27. How large a sample n do you need so that a 99% confidence interval for the mean has a margin of error of at most 1.5?

σ = 27E = 1.599%
n =

Answer key

  1. 1. E = 1.44
  2. 2. σ = 12.04
  3. 3. E = 0.6646 mmHg
  4. 4. lower limit = 55.31
  5. 5. n = 2601
  6. 6. n = 2150

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