1.Easy
A company claims that a proportion of 0.75 of its customers are satisfied. In a random survey of 400 customers, 310 say they are satisfied. Find the test statistic z for H₀: p = 0.75.
p₀ = 0.75n = 400x = 310
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 64 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 = 64
z =
3.Medium
A sample of 100 students has a mean score of 119.5 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 120.
μ₀ = 120x̄ = 119.5s = 5n = 100
t =
4.Medium
Two teaching methods are compared. Group 1: 10 students, mean score 27, standard deviation 9. Group 2: 7 students, mean score 37.2, standard deviation 2.5. Assume equal population variances and use the pooled two-sample t test. Find the test statistic t for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (group 1 minus group 2).
n₁ = 10x̄₁ = 27s₁ = 9n₂ = 7x̄₂ = 37.2s₂ = 2.5
t =
5.Hard
In a trial, 30 of 200 patients on treatment A recover, and 33 of 300 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 30n₁ = 200x₂ = 33n₂ = 300
z =
6.Hard
A sample of 16 measurements has mean 111.9. The population standard deviation is 12. Find the upper limit U of the 95% confidence interval for the mean.
x̄ = 111.9σ = 12n = 1695%
U =
Answer key
- 1. z = 1.155
- 2. z = 2.4
- 3. t = −1
- 4. t = −2.895
- 5. z = 1.32
- 6. U = 117.8
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