1.Easy
A company claims that a proportion of 0.2 of its customers are satisfied. In a random survey of 400 customers, 62 say they are satisfied. Find the test statistic z for H₀: p = 0.2.
p₀ = 0.2n = 400x = 62
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is set to fill packs with a mean of 75 g; you suspect it underfills. The standard deviation is known to be 12 g. You will weigh a sample of 36 packs and test H₀: μ = 75 against H₁: μ < 75 at α = 0.01. Below which sample mean x̄c will you reject H₀?
μ₀ = 75 gσ = 12 gn = 36α = 0.01
x̄c = g
3.Medium
A sample of 25 students has a mean score of 90.7 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 100.
μ₀ = 100x̄ = 90.7s = 15n = 25
t =
4.Medium
A sample of 25 students has a mean score of 205.8 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 200.
μ₀ = 200x̄ = 205.8s = 10n = 25
t =
5.Hard
In a trial, 60 of 120 patients on treatment A recover, and 130 of 200 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 60n₁ = 120x₂ = 130n₂ = 200
z =
6.Hard
A one-sided z test of H₀: μ = 500 against H₁: μ > 500 is done at α = 0.05 with a sample of 25; the standard deviation is known to be 5. In reality the mean is 501.2. Find the power 1 − β of the test in percent.
μ₀ = 500μ = 501.2σ = 5n = 25α = 0.05
1 − β = %
Answer key
- 1. z = −2.25
- 2. x̄c = 70.35 g
- 3. t = −3.1
- 4. t = 2.9
- 5. z = −2.645
- 6. 1 − β = 32.82 %
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