Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Analyze Phase: Hypothesis Testing 1

Question 1

A Black Belt runs a hypothesis test and obtains a p-value of 0.03 with alpha set at 0.05. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis because the p-value is less than alpha

Answer

When the p-value is less than the chosen significance level (alpha), the evidence against the null hypothesis is sufficient to reject it. Here, 0.03 < 0.05, so H₀ is rejected. Note that we 'fail to reject' or 'reject' H₀ — we never formally 'accept' it.

Question 2

A Black Belt measures cycle time on the same 20 workstations before and after a process change. Which hypothesis test is most appropriate?

Accepted Answer

Paired t-test

Answer

A paired t-test is used when the same subjects or units are measured twice (before and after). It accounts for the natural correlation between paired observations, reducing variability and increasing statistical power compared to treating the groups as independent.

Question 3

Before applying a parametric hypothesis test such as a t-test, a Black Belt should use the Anderson-Darling test to verify which assumption?

Accepted Answer

That the data is approximately normally distributed

Answer

Parametric tests assume the underlying data (or residuals) are approximately normally distributed. The Anderson-Darling test is one of the most common normality tests used in Minitab and Six Sigma workflows to verify this assumption before proceeding.

Question 4

A Black Belt increases the significance level (alpha) from 0.05 to 0.10. What is the direct statistical consequence?

Accepted Answer

The probability of a Type I error increases

Answer

Alpha is by definition the probability of committing a Type I error (rejecting a true null hypothesis). Raising alpha from 0.05 to 0.10 directly raises the Type I error rate. As a side effect, power increases and the Type II error rate decreases, but the primary direct consequence is an increased Type I error probability.

Question 5

A Black Belt wants to determine whether defect type (scratch, dent, discoloration) is independent of production shift (day, evening, night). Which test is most appropriate?

Accepted Answer

Chi-square test of independence

Answer

The chi-square test of independence evaluates whether two categorical variables are associated by comparing observed cell frequencies to expected frequencies under the assumption of independence. Both defect type and production shift are categorical, making this the correct choice.

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Analyze Phase: Hypothesis Testing 1