Master statistical hypothesis testing with 15 comprehensive questions covering basic concepts, test selection, calculations, and advanced topics like GLRT and multiple testing.
15
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Basic Concepts
1 questions
Question 1: Type I Error Definition
What is the definition of a Type I error in hypothesis testing?...
Beginner
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Test Selection
1 questions
Question 2: Choosing Between U-test and T-test
For testing a population mean μ from a normal distribution, when should you use a U-test (Z-test) in...
Beginner
Not attempted
U-Test
1 questions
Question 3: U-Test Calculation
A sample of n=25 items from N(μ,16) has sample mean x̄=52. Test H₀: μ=50 vs H₁: μ≠50 at α=0.05. What...
Intermediate
Not attempted
T-Test
1 questions
Question 4: T-Test Degrees of Freedom
In a one-sample t-test with sample size n=20, what are the degrees of freedom for the test statistic...
Intermediate
Not attempted
P-value
1 questions
Question 5: P-value Interpretation
If a hypothesis test yields P-value = 0.03 and the significance level is α = 0.05, what should you c...
Intermediate
Not attempted
Chi-Square Test
1 questions
Question 6: Variance Test Statistic
For testing H₀: σ²=4 vs H₁: σ²≠4 with sample size n=10 and sample variance s²=6.25, what is the chi-...
Intermediate
Not attempted
Two-Sample Tests
1 questions
Question 7: Pooled Variance Calculation
Two independent samples: n₁=12, s₁²=8, n₂=15, s₂²=12. What is the pooled variance s²ₚ for a two-samp...
Advanced
Not attempted
Power and Sample Size
1 questions
Question 8: Statistical Power
If the power of a test is 0.85, what is the probability of Type II error?...
Advanced
Not attempted
GLRT
1 questions
Question 9: Likelihood Ratio Test
In a generalized likelihood ratio test, what does λ(x̃) represent?...
Advanced
Not attempted
Multiple Testing
1 questions
Question 10: Bonferroni Correction
If you perform 5 independent hypothesis tests, each at significance level α=0.05, and want to contro...
Advanced
Not attempted
Effect Size
1 questions
Question 11: Practical vs Statistical Significance
A large-sample study (n=10,000) finds a statistically significant difference (P<0.001) between two g...
Intermediate
Not attempted
Assumptions
1 questions
Question 12: Test Assumptions
Which assumption is NOT required for a one-sample t-test?...
Intermediate
Not attempted
Critical Values
1 questions
Question 13: Two-sided vs One-sided Tests
For a two-sided test at α=0.05 using standard normal distribution, the critical values are ±1.96. Wh...
Intermediate
Not attempted
Confidence Intervals
1 questions
Question 14: CI-Hypothesis Test Duality
A 95% confidence interval for μ is [48.2, 51.8]. Which null hypotheses would be rejected at α=0.05?...
Advanced
Not attempted
F-Test
1 questions
Question 15: Variance Ratio Test
Two independent samples: n₁=21, s₁²=15, n₂=16, s₂²=10. For testing H₀: σ₁²=σ₂² vs H₁: σ₁²≠σ₂², what ...
Advanced
Not attempted
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