1.Easy
A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 12 mL. A sample of 49 bottles has a mean of 79.11 mL. Find the test statistic z for H₀: μ = 75.
μ₀ = 75 mLx̄ = 79.11 mLσ = 12 mLn = 49
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is set to fill packs with a mean of 120 g; you suspect it underfills. The standard deviation is known to be 4 g. You will weigh a sample of 16 packs and test H₀: μ = 120 against H₁: μ < 120 at α = 0.01. Below which sample mean x̄c will you reject H₀?
μ₀ = 120 gσ = 4 gn = 16α = 0.01
x̄c = g
3.Medium
The mean of a population is claimed to be 50; the population standard deviation is known to be 9. A random sample of 36 observations has a mean of 52.4. Test H₀: μ = 50 against H₁: μ > 50. Find the p-value p.
μ₀ = 50σ = 9n = 36x̄ = 52.4H₁: μ > μ₀
p =
4.Medium
Two teaching methods are compared. Group 1: 15 students, mean score 44.5, standard deviation 2. Group 2: 6 students, mean score 40.7, standard deviation 7. 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 = 15x̄₁ = 44.5s₁ = 2n₂ = 6x̄₂ = 40.7s₂ = 7
t =
5.Hard
A sample of 16 measurements has mean 77.3. The population standard deviation is 4. Find the lower limit L of the 90% confidence interval for the mean.
x̄ = 77.3σ = 4n = 1690%
L =
6.Hard
How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 1? The standard deviation is 10. Find the smallest sample size n.
σ = 10E = 199%
n =
Answer key
- 1. z = 2.397
- 2. x̄c = 117.7 g
- 3. p = 0.0548
- 4. t = 1.976
- 5. L = 75.66
- 6. n = 664
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