DSE Statistical Inference and Hypothesis Testing 2

Question 1

A researcher sets α = 0.01 instead of α = 0.05. What is the direct consequence?

Accepted Answer

Reduced probability of a Type I error

Answer

Lowering α makes the rejection region smaller, directly reducing the probability of falsely rejecting a true null hypothesis (Type I error).

Question 2

Which condition must hold for the Central Limit Theorem to justify using a z-test on non-normal data?

Accepted Answer

Sample size must be sufficiently large (typically n ≥ 30)

Answer

The CLT states that sample means approach normality as n grows, making large samples the key requirement for z-tests on non-normal populations.

Question 3

A 95% confidence interval for a mean is (12.3, 17.7). What is the correct interpretation?

Accepted Answer

If we repeated this procedure many times, 95% of such intervals would contain the true mean

Answer

Confidence intervals are a long-run frequency statement about the procedure, not a probability statement about a fixed (unknown) parameter.

Question 4

The Bonferroni correction addresses which problem in multiple hypothesis testing?

Accepted Answer

Inflated familywise Type I error rate

Answer

Running many tests at α = 0.05 each inflates the chance of at least one false positive; Bonferroni divides α by the number of tests to control the familywise error rate.

Question 5

A paired t-test is preferred over an independent samples t-test when:

Accepted Answer

Each observation in one group is naturally matched to one in the other

Answer

Pairing (e.g., before/after measurements on the same subject) removes between-subject variability, increasing power via the paired design.

DSE - Data Science Practice Test

DSE - Data Science Practice Test

DSE Statistical Inference and Hypothesis Testing 2