MS-DS Master of Data science Statistical Inference Concepts 4

Question 1

In a chi-square goodness-of-fit test, the test statistic is large when:

Accepted Answer

Observed frequencies deviate substantially from expected frequencies

Answer

The chi-square statistic Σ(O−E)²/E is large when observed counts differ greatly from what the null hypothesis predicts.

Question 2

The delta method is used to approximate the variance of g(X̄) when:

Accepted Answer

g is a smooth (differentiable) function and n is large

Answer

The delta method uses a first-order Taylor expansion of g around μ; it requires g to be differentiable and works well for large n via the CLT.

Question 3

A p-value of 0.001 in a study with n = 10,000 primarily reflects:

Accepted Answer

A very small effect size that is detectable only due to the huge sample

Answer

With n = 10,000, even tiny effects produce very small p-values; the p-value conflates effect size with sample size.

Question 4

In hypothesis testing, which error is controlled directly by setting the significance level α?

Accepted Answer

Type I error (rejecting a true H₀)

Answer

The significance level α is defined as the maximum acceptable probability of a Type I error (false positive).

Question 5

The Rao-Blackwell theorem states that if T is a sufficient statistic and U is an unbiased estimator, then E[U|T] is:

Accepted Answer

Unbiased and has variance no greater than that of U

Answer

Conditioning an unbiased estimator on a sufficient statistic yields an unbiased estimator with equal or lower variance — the Rao-Blackwell improvement.

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 4