Statistics Case Studies & Practical Application 3

Question 1

A food company conducts an A/B test on two package designs. Design A (n=500) gets 120 purchases; Design B (n=500) gets 145 purchases. A chi-square test yields p=0.04. What is the correct business decision?

Accepted Answer

Switch to Design B because it is statistically significantly better

Answer

With p=0.04 < 0.05, the difference is statistically significant, supporting adoption of Design B which outperformed Design A.

Question 2

A meteorologist models monthly rainfall using a Poisson distribution. Last month had 14 rain events; the historical mean is 10. What does this data suggest?

Accepted Answer

The month's rainfall was above average but within plausible Poisson variation

Answer

For a Poisson distribution with λ=10, values of 14 are uncommon but not impossible, as the standard deviation is √10 ≈ 3.16.

Question 3

A sociologist uses stratified random sampling to study income across 4 age groups. She samples proportionally: 60 from ages 18-30, 90 from 31-50, 80 from 51-65, and 20 from 65+. What is the primary advantage of this approach over simple random sampling?

Accepted Answer

It ensures each age group is adequately represented for group-level comparisons

Answer

Stratified sampling ensures representation from all subgroups, enabling more precise estimates within and comparisons across strata.

Question 4

A factory monitors defect rates daily. Over 30 days, the p-chart shows all points within control limits but exhibiting a steady downward trend. What does this pattern suggest?

Accepted Answer

A systematic non-random pattern signals a potential special cause

Answer

A consistent trend, even within control limits, is a non-random pattern (run rule violation) suggesting an assignable cause is present.

Question 5

A clinical trial uses a crossover design where each patient receives both the drug and placebo in randomized order. What statistical test is most appropriate for comparing outcomes?

Accepted Answer

Paired samples t-test

Answer

A crossover design produces paired observations from the same subjects, so a paired t-test accounts for within-subject correlation and reduces variability.

Statistics Practice Test

Statistics Practice Test

Statistics Case Studies & Practical Application 3