1.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 10 mL. A sample of 64 bottles has a mean of 48.88 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 48.88 mLσ = 10 mLn = 64
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 8 mL. A sample of 49 bottles has a mean of 502.4 mL. Find the test statistic z for H₀: μ = 500.
μ₀ = 500 mLx̄ = 502.4 mLσ = 8 mLn = 49
z =
3.Medium
A sample of 49 students has a mean score of 500.9 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 500.
μ₀ = 500x̄ = 500.9s = 5n = 49
t =
4.Medium
Two production lines make the same part. Line 1: a sample of 100 parts has mean length 119 mm, and the line's known standard deviation is 10 mm. Line 2: a sample of 80 parts has mean 123.3 mm, known standard deviation 17 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 100x̄₁ = 119 mmσ₁ = 10 mmn₂ = 80x̄₂ = 123.3 mmσ₂ = 17 mm
z =
5.Hard
A sample of 100 measurements has mean 100.9. The population standard deviation is 5. Find the lower limit L of the 90% confidence interval for the mean.
x̄ = 100.9σ = 5n = 10090%
L =
6.Hard
In a trial, 163 of 250 patients on treatment A recover, and 231 of 300 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 163n₁ = 250x₂ = 231n₂ = 300
z =
Answer key
- 1. z = −0.896
- 2. z = 2.1
- 3. t = 1.26
- 4. z = −2.002
- 5. L = 100.1
- 6. z = −3.057
Full step-by-step solutions: practise this topic on examproblems.com.