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 machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 10 mL. A sample of 16 bottles has a mean of 81 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 81 mLσ = 10 mLn = 16

z =

2.Easy

A machine is set to fill packs with a mean of 500 g; you suspect it underfills. The standard deviation is known to be 8 g. You will weigh a sample of 36 packs and test H₀: μ = 500 against H₁: μ < 500 at α = 0.01. Below which sample mean x̄_c will you reject H₀?

μ₀ = 500 gσ = 8 gn = 36α = 0.01

x̄_c = g

3.Medium

A sample of 36 students has a mean score of 97.07 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 97.07s = 8n = 36

t =

4.Medium

A sample of 100 students has a mean score of 48.76 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 48.76s = 4n = 100

t =

5.Hard

A sample of 81 measurements has mean 499.5. The population standard deviation is 4. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 499.5σ = 4n = 8199%

L =

6.Hard

A one-sided z test at α = 0.05 must detect a shift of the mean of 1.5 units with a power of 90%. The standard deviation is 4. Find the minimum sample size n.

α = 0.05power = 90%δ = 1.5σ = 4z_α = 1.645z_β = 1.282

n =

Answer key

1. z = 2.4
2. x̄_c = 496.9 g
3. t = −2.198
4. t = −3.1
5. L = 498.4
6. n = 61

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