1.Easy
A company claims that a proportion of 0.2 of its customers are satisfied. In a random survey of 500 customers, 73 say they are satisfied. Find the test statistic z for H₀: p = 0.2.
p₀ = 0.2n = 500x = 73
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 12 mL. A sample of 100 bottles has a mean of 123.5 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 123.5 mLσ = 12 mLn = 100
z =
3.Medium
A sample of 49 students has a mean score of 51.37 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 50.
μ₀ = 50x̄ = 51.37s = 4n = 49
t =
4.Medium
Two production lines make the same part. Line 1: a sample of 50 parts has mean length 103.5 mm, and the line's known standard deviation is 5 mm. Line 2: a sample of 50 parts has mean 106.1 mm, known standard deviation 7 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 50x̄₁ = 103.5 mmσ₁ = 5 mmn₂ = 50x̄₂ = 106.1 mmσ₂ = 7 mm
z =
5.Hard
A sample of 81 measurements has mean 121.3. The population standard deviation is 15. Find the lower limit L of the 95% confidence interval for the mean.
x̄ = 121.3σ = 15n = 8195%
L =
6.Hard
A sample of 64 measurements has mean 120.5. The population standard deviation is 12. Find the lower limit L of the 95% confidence interval for the mean.
x̄ = 120.5σ = 12n = 6495%
L =
Answer key
- 1. z = −3.019
- 2. z = 2.917
- 3. t = 2.397
- 4. z = −2.137
- 5. L = 118
- 6. L = 117.6
Full step-by-step solutions: practise this topic on examproblems.com.