Hypothesis tests & confidence intervals worksheet with answers

Free printable Hypothesis tests & 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

A company claims that a proportion of 0.7 of its customers are satisfied. In a random survey of 400 customers, 262 say they are satisfied. Find the test statistic z for H₀: p = 0.7.

p₀ = 0.7n = 400x = 262

z =

2.Easy

A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 10 mL. A sample of 100 bottles has a mean of 75.7 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 75.7 mLσ = 10 mLn = 100

z =

3.Medium

A sample of 81 students has a mean score of 73.04 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 73.04s = 8n = 81

t =

4.Medium

The mean of a population is claimed to be 50; the population standard deviation is known to be 15. A random sample of 36 observations has a mean of 43.95. Test H₀: μ = 50 against H₁: μ ≠ 50. Find the p-value p.

μ₀ = 50σ = 15n = 36x̄ = 43.95H₁: μ ≠ μ₀

p =

5.Hard

A sample of 25 measurements has mean 120.3. The population standard deviation is 15. Find the lower limit L of the 90% confidence interval for the mean.

x̄ = 120.3σ = 15n = 2590%

L =

6.Hard

A one-sided z test at α = 0.01 must detect a shift of the mean of 4 units with a power of 95%. The standard deviation is 14. Find the minimum sample size n.

α = 0.01power = 95%δ = 4σ = 14z_α = 2.326z_β = 1.645

n =

Answer key

1. z = −1.964
2. z = 0.7
3. t = −2.205
4. p = 0.01552
5. L = 115.4
6. n = 194

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