Statistics Case Studies & Practical Application 2

Question 1

A pharmaceutical company tests a new drug on 200 patients split evenly between treatment and placebo groups. The treatment group shows a 15% improvement vs 8% for placebo (p=0.03). What is the most appropriate conclusion?

Accepted Answer

The drug shows statistically significant but not necessarily clinically meaningful improvement

Answer

Statistical significance (p=0.03) does not automatically imply clinical meaningfulness; effect size and practical context must also be evaluated.

Question 2

A quality control engineer samples 50 bolts per hour from a production line and plots X-bar and R charts. She notices 3 consecutive points above the upper control limit. What action is most appropriate?

Accepted Answer

Investigate and identify the assignable cause of variation

Answer

Points outside control limits signal a special (assignable) cause that must be identified and corrected before resuming normal production.

Question 3

An economist uses linear regression to predict housing prices based on square footage. The R² is 0.62. What does this indicate?

Accepted Answer

62% of variation in housing prices is explained by square footage

Answer

R² represents the proportion of variance in the dependent variable explained by the independent variable(s) in the model.

Question 4

A polling firm surveys 1,000 likely voters and finds 52% favor Candidate A with a margin of error of ±3%. A rival poll of 500 voters shows 54% for Candidate A. Which poll is more reliable?

Accepted Answer

The first poll because larger sample sizes yield smaller margins of error

Answer

Larger sample sizes reduce sampling error and produce narrower confidence intervals, making the 1,000-person poll more reliable.

Question 5

A school district compares test scores of students who attended summer school (n=80, mean=72) vs those who did not (n=120, mean=68). An independent samples t-test gives p=0.07. What is the best interpretation?

Accepted Answer

The difference is not statistically significant at the 0.05 level but may warrant further study

Answer

A p-value of 0.07 exceeds the conventional α=0.05 threshold, so we fail to reject the null hypothesis, though the result may still have practical interest.

Statistics Practice Test

Statistics Practice Test

Statistics Case Studies & Practical Application 2