Statistics Case Studies & Practical Application 5

Question 1

A sports analyst examines whether home-field advantage exists by testing if home teams win more than 50% of games across 500 games. 275 home wins are observed. What test is appropriate?

Accepted Answer

One-sample z-test for a proportion against H₀: p=0.50

Answer

Testing a single observed proportion against a known hypothesized value (0.50) calls for a one-sample z-test for proportions.

Question 2

A neuroscientist measures reaction times before and after caffeine intake for 15 subjects. Which test is most appropriate?

Accepted Answer

Paired t-test

Answer

The same subjects are measured twice (before and after), creating dependent pairs, which is handled by the paired t-test to control for individual variability.

Question 3

A data scientist splits a dataset 80/20 into training and test sets, fits a model on training data, and evaluates on the test set. The test set accuracy is 78%. What does this metric measure?

Accepted Answer

The model's ability to generalize to unseen data

Answer

Evaluating on a held-out test set estimates how well the model generalizes to new, unseen observations not used during training.

Question 4

A researcher calculates Cohen's d = 0.82 when comparing two teaching methods. How should this effect size be interpreted?

Accepted Answer

Large effect — the methods differ by nearly one standard deviation

Answer

Cohen's d = 0.82 falls in the 'large' range (d > 0.8), indicating the group means differ by approximately 0.82 standard deviations.

Question 5

A supply chain manager tracks weekly inventory levels over 2 years and notices a strong upward trend. She fits a simple linear regression with time as the predictor. What assumption violation is most likely?

Accepted Answer

Autocorrelation: residuals from time-series data are often correlated across time

Answer

Time-series data often violates the independence assumption because consecutive residuals are correlated (autocorrelation), inflating the significance of regression estimates.

Statistics Practice Test

Statistics Practice Test

Statistics Case Studies & Practical Application 5