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 = 64, σ = 10L = ?Ux̄ = 44E90%

A sample of 64 measurements has mean 44. The population standard deviation is known to be 10. Find the lower limit of the 90% confidence interval for the mean.

n = 64x̄ = 44σ = 1090%
lower limit =
2.Easy
n = 80, σ = 29L = ?Ux̄ = 99E90%

A sample of 80 measurements has mean 99. The population standard deviation is known to be 29. Find the lower limit of the 90% confidence interval for the mean.

n = 80x̄ = 99σ = 2990%
lower limit =
3.Medium
n = 9, s = 14LUx̄ = 39.5E = ?99%

A sample of 9 items has mean 39.5 and standard deviation s = 14. The population is roughly normal. Find the margin of error E of a 99% confidence interval for the mean.

n = 9x̄ = 39.5s = 1499%t(8) = 3.355
E =
4.Medium
n = 11, sd​ = 7.30L = ?Ud̄ = −2E99%

The blood pressure of 11 patients is measured before and after a treatment. The differences d = before − after (mmHg) have mean −2 and standard deviation 7.3. Find the lower limit of the 99% confidence interval for the mean difference.

n = 11d̄ = −2sd = 7.399%t(10) = 3.169
lower limit = mmHg
5.Hard
σ = 22, n = ?x̄ − Ex̄ + Ex̄E = 190%

The population standard deviation is 22. 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 = 22E = 190%
n =
6.Hard
σ = 23, n = ?x̄ − Ex̄ + Ex̄E = 195%

The population standard deviation is 23. How large a sample n do you need so that a 95% confidence interval for the mean has a margin of error of at most 1?

σ = 23E = 195%
n =

Answer key

  1. 1. lower limit = 41.94
  2. 2. lower limit = 93.67
  3. 3. E = 15.66
  4. 4. lower limit = −8.975 mmHg
  5. 5. n = 1310
  6. 6. n = 2033

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