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 = 49, σ = 22L = ?Ux̄ = 74E95%

A sample of 49 measurements has mean 74. The population standard deviation is known to be 22. Find the lower limit of the 95% confidence interval for the mean.

n = 49x̄ = 74σ = 2295%
lower limit =
2.Easy
n = 100, σ = 11L = ?Ux̄ = 56.5E90%

A sample of 100 measurements has mean 56.5. The population standard deviation is known to be 11. Find the lower limit of the 90% confidence interval for the mean.

n = 100x̄ = 56.5σ = 1190%
lower limit =
3.Medium
μ₁ − μ₂0LUx̄₁ − x̄₂E = ?95%

The battery life of two phone models is compared. Model 1: 40 phones, mean 62.5 h, known standard deviation 18 h. Model 2: 40 phones, mean 52 h, known standard deviation 10 h. Find the margin of error E of the 95% confidence interval for μ₁ − μ₂.

n₁ = 40x̄₁ = 62.5 hσ₁ = 18 hn₂ = 40x̄₂ = 52 hσ₂ = 10 h95%
E = h
4.Medium
x̄E₁ = 11.499%, n = 36x̄E₂ = ?95%, n = 36

A 99% confidence interval for a mean, based on 36 observations and a known σ, has a margin of error of 11.4. What is the margin of error E₂ of a 95% interval from the same data?

99%n₁ = 36E₁ = 11.495%
E₂ =
5.Hard
σ = 25, n = ?x̄ − Ex̄ + Ex̄E = 499%

The population standard deviation is 25. 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 4?

σ = 25E = 499%
n =
6.Hard
n = 20σ = ?Us = 10.395%

The diameters of 20 machined shafts have a sample standard deviation of 10.3 µm. Assuming the diameters are normally distributed, find the lower limit σ of the 95% confidence interval for the population standard deviation. With df = 19, 2.5% of the χ² distribution lies below 8.907 and 2.5% lies above 32.852.

n = 20s = 10.3 µmχ² = 8.907, 32.852
σ = µm

Answer key

  1. 1. lower limit = 67.84
  2. 2. lower limit = 54.69
  3. 3. E = 6.381 h
  4. 4. E₂ = 8.674
  5. 5. n = 260
  6. 6. σ = 7.833 µm

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