Quiz 3 – Statistical Analysis

A Green Belt tests whether a process defect proportion differs from a specified historical value. Which type of hypothesis test is most directly appropriate? *

Proportion test

Mean test

Regression analysis

Measurement System Analysis

In hypothesis testing, what is the correct decision when the p-value is less than or equal to the chosen significance level α? *

Reject the null hypothesis

Fail to reject the null hypothesis

Accept the null hypothesis as proven

Increase the significance level until the result changes

A Green Belt compares the average cycle time from Machine A with the average cycle time from Machine B using independent samples. Which analysis is most directly suited to this comparison? *

Two-sample mean test

One-sample proportion test

Chi-square goodness-of-fit test

Scatter diagram

A study compares the defect proportions of Shift A and Shift B. Shift A has a defect rate of 4% and Shift B has a defect rate of 7%. Which type of test is appropriate for evaluating whether the proportions differ? *

One-sample mean test

Two-sample proportion test

Paired mean test

Simple linear regression

A scatter diagram shows that as machine temperature increases, the number of defects generally decreases. What does this visual pattern indicate? *

A possible negative relationship

A proven causal relationship

A guaranteed statistically significant relationship

No relationship between the variables

The Pearson correlation coefficient between two numerical variables is r = −0.90. What does this value indicate? *

A strong negative linear association

A strong positive linear association

No linear association

A perfect causal relationship

A regression model is Ŷ = 50 + 2X. What is the interpretation of the slope? *

Y equals 50 whenever X increases by one unit

Each one-unit increase in X is associated with an estimated two-unit increase in Y

Each two-unit increase in X causes Y to decrease by one unit

The model explains 2% of the variation in Y

A regression model has R² = 0.64. Which interpretation is most appropriate? *

About 64% of the observed variation in Y is explained by the fitted model

The model proves that X causes 64% of Y

The correlation must equal 0.64 in every regression context

The model predicts every future observation with 64% accuracy

A Green Belt finds a strong correlation between two process variables. Which conclusion is scientifically appropriate? *

The first variable is proven to be the root cause

The variables are associated, but causation still requires further investigation

The second variable must be the root cause

The correlation makes process knowledge unnecessary

A regression analysis shows a statistically significant slope, but the practical effect is very small. What should the Green Belt do? *

Consider statistical significance together with practical significance and process context

Declare the variable a critical root cause solely because p < α

Ignore the statistical result completely

Treat the regression equation as proof of causation