Analyse: Data & Hypothesis Testing

In hypothesis testing, what is the correct decision rule when the calculated p-value is less than the chosen significance level alpha?

• A Accept the null hypothesis as proven true
• B Reject the null hypothesis ✓
• C Increase the sample size and retest
• D Fail to reject the null hypothesis

Answer: When p is less than alpha, the result is statistically significant and the null hypothesis is rejected in favour of the alternative.

A Type I error in hypothesis testing is best described as:

• A Rejecting a null hypothesis that is actually true ✓
• B Choosing the wrong statistical test for the data
• C Using a sample that is too small to detect an effect
• D Failing to reject a null hypothesis that is actually false

Answer: A Type I error (false positive) occurs when a true null hypothesis is incorrectly rejected; its probability equals the significance level alpha.

A Type II error occurs when an analyst:

• A Fails to reject a false null hypothesis ✓
• B Sets the significance level too low
• C Confuses correlation with causation
• D Rejects a true null hypothesis

Answer: A Type II error (false negative) is failing to reject a null hypothesis that is actually false; its probability is denoted beta and 1 minus beta is the test's power.

Which statistical test is most appropriate for comparing the means of three or more independent groups simultaneously?

• A Chi-square test of independence
• B One-way ANOVA ✓
• C Paired t-test
• D Two-sample t-test

Answer: One-way ANOVA tests whether the means of three or more groups are equal while controlling the overall Type I error rate, unlike running multiple t-tests.

A team wants to know whether shift (day/evening/night) is associated with defect category (scratch/dent/crack). Which test is most appropriate?

• A Paired t-test
• B Chi-square test of independence ✓
• C One-sample t-test
• D Simple linear regression

Answer: The chi-square test of independence assesses whether two categorical variables are associated, which fits comparing shift against defect category counts.

A two-sample t-test is the appropriate analysis when you want to:

• A Test for association between two categorical variables
• B Compare the variances of five processes
• C Model a curved relationship between two continuous variables
• D Compare the means of two independent groups on a continuous measure ✓

Answer: The two-sample (independent) t-test compares the means of two separate groups measured on a continuous scale.