Explanation

This question tests understanding of Type I and Type II errors in hypothesis testing.

Key Concepts:

1. Type I Error (α error): Rejecting a true null hypothesis (false positive)
2. Type II Error (β error): Failing to reject a false null hypothesis (false negative)
3. Power of a test: Probability of correctly rejecting a false null hypothesis (1 - β)

Analysis:

• The scenario describes "fails to reject a false null hypothesis"
• This is the exact definition of a Type II error
• A Type I error would be "rejecting a true null hypothesis"
• While a test with little power is more likely to make Type II errors, the specific result described is a Type II error itself

Correct Answer: B (Type II error)

Additional Context:

• Type I error rate is denoted by α (significance level)
• Type II error rate is denoted by β
• Power = 1 - β (probability of correctly rejecting false null)
• The relationship between errors: Decreasing α (Type I error) typically increases β (Type II error) for a given sample size