DSE Statistical Inference and Hypothesis Testing 3

Question 1

What does the power of a hypothesis test measure?

Accepted Answer

Probability of rejecting H₀ when H₀ is false

Answer

Power = 1 − β, where β is the Type II error rate; it is the probability of correctly detecting a true effect.

Question 2

A one-sample chi-squared test is used to test whether observed category frequencies match:

Accepted Answer

Expected frequencies from a theoretical distribution

Answer

The chi-squared goodness-of-fit test compares observed counts to expected counts derived from a hypothesized distribution.

Question 3

Increasing sample size while keeping α fixed will generally:

Accepted Answer

Narrow the confidence interval and increase power

Answer

Larger samples reduce standard error, producing narrower confidence intervals and greater ability to detect true effects (higher power).

Question 4

The Kolmogorov-Smirnov test is primarily used to:

Accepted Answer

Test whether a sample comes from a specified distribution

Answer

The KS test measures the maximum distance between an empirical CDF and a theoretical CDF to assess distributional fit.

Question 5

Which scenario correctly illustrates a Type II error?

Accepted Answer

Failing to detect a real difference between two drug dosages

Answer

A Type II error (false negative) occurs when we fail to reject H₀ even though H₁ is actually true.

DSE - Data Science Practice Test