Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 4

Question 1

The Wilcoxon signed-rank test is the nonparametric equivalent of:

Accepted Answer

One-sample or paired t-test

Answer

The Wilcoxon signed-rank test handles one-sample or paired data, making it the nonparametric counterpart of the one-sample and paired t-tests.

Question 2

A Black Belt finds a statistically significant difference but the effect size (Cohen's d) is 0.08. This result is best described as:

Accepted Answer

Statistically significant but practically trivial

Answer

Cohen's d of 0.08 is far below the conventional small-effect threshold of 0.2, indicating the detected difference is unlikely to be practically meaningful.

Question 3

In a two-proportion z-test, the pooled proportion p̂ is used because:

Accepted Answer

Under H₀ the two populations share a common proportion

Answer

Under the null hypothesis of equal proportions, both samples estimate the same population proportion, so a pooled estimate is the best single estimate to use in the standard error.

Question 4

Which test statistic is used in a chi-square goodness-of-fit test?

Accepted Answer

Σ (O − E)² / E

Answer

The chi-square statistic sums the squared differences between observed (O) and expected (E) frequencies, divided by expected frequency, across all categories.

Question 5

A Black Belt sets α = 0.01 instead of α = 0.05. This decision:

Accepted Answer

Reduces power and reduces Type I error risk

Answer

Tightening alpha reduces the chance of a false positive (Type I error) but makes it harder to detect real effects, thereby reducing power.

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Advanced Hypothesis Testing 4