MS-DS Master of Data science Statistical Inference Concepts 2

Question 1

A 95% confidence interval for the mean is [42, 58]. What is the correct interpretation?

Accepted Answer

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

Answer

A confidence interval is a procedure: 95% of intervals constructed this way will capture the true parameter, not a probability statement about one specific interval.

Question 2

Which of the following is a consequence of increasing the sample size in hypothesis testing while keeping α fixed?

Accepted Answer

Type II error rate decreases (power increases)

Answer

Larger samples reduce variance, making the test more sensitive and increasing statistical power (decreasing Type II error).

Question 3

In a two-sided t-test with H₀: μ = 10 and a test statistic t = 2.1 (df=25), the p-value is approximately 0.046. At α = 0.05, what is the conclusion?

Accepted Answer

Reject H₀ because p < α

Answer

Since p ≈ 0.046 < 0.05 = α, we reject the null hypothesis at the 5% significance level.

Question 4

The Neyman-Pearson lemma establishes that the likelihood ratio test is:

Accepted Answer

The most powerful test for a simple null versus a simple alternative

Answer

The Neyman-Pearson lemma proves that the likelihood ratio test is the most powerful test for comparing two simple (point) hypotheses.

Question 5

A researcher uses bootstrapping to estimate the standard error of the median. What does this method fundamentally rely on?

Accepted Answer

Resampling with replacement from the observed data to approximate the sampling distribution

Answer

Bootstrapping treats the empirical distribution as a proxy for the population and resamples with replacement to build an approximate sampling distribution.

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 2