MS-DS Master of Data science Statistical Inference Concepts 3

Question 1

A study finds a statistically significant result with p = 0.03, but the effect size is d = 0.05. What is the most appropriate conclusion?

Accepted Answer

The effect is statistically significant but likely of negligible practical importance

Answer

With large enough samples, even trivially small effects become statistically significant; effect size (d = 0.05) indicates negligible practical importance.

Question 2

The Fisher information I(θ) quantifies:

Accepted Answer

The expected curvature of the log-likelihood, reflecting how much data informs about θ

Answer

Fisher information measures how sensitive the log-likelihood is to changes in θ, capturing how much the data can tell us about the parameter.

Question 3

When performing multiple hypothesis tests simultaneously, the Bonferroni correction adjusts α by:

Accepted Answer

Dividing α by the number of tests

Answer

Bonferroni sets the per-test significance level to α/m (where m is the number of tests) to control the familywise error rate.

Question 4

Which of the following best describes a sufficient statistic for parameter θ?

Accepted Answer

A statistic T(X) such that the conditional distribution of X given T does not depend on θ

Answer

A sufficient statistic captures all information in the sample about θ; knowing T(X) renders the rest of the data irrelevant for estimating θ.

Question 5

The power of a test is defined as:

Accepted Answer

The probability of rejecting H₀ when H₀ is false

Answer

Power = 1 − β = P(reject H₀ | H₀ is false), measuring a test's ability to detect a true effect.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Statistical Inference Concepts 3