Statistics Case Studies & Practical Application 2 — Questions and Answers
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?
- The drug is clinically significant because p < 0.05
- The drug shows statistically significant but not necessarily clinically meaningful improvement (Correct answer)
- The study proves the drug works for all patients
- The placebo effect invalidates the results
Correct answer: The drug shows statistically significant but not necessarily clinically meaningful improvement
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?
- Increase the sample size to reduce variability
- Investigate and identify the assignable cause of variation (Correct answer)
- Recalculate control limits using the new data
- Shut down the production line immediately
Correct answer: Investigate and identify the assignable cause of variation
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?
- 62% of variation in housing prices is explained by square footage (Correct answer)
- Square footage causes 62% of the change in housing price
- The model predicts housing prices correctly 62% of the time
- 62% of the data points fall within the confidence interval
Correct answer: 62% of variation in housing prices is explained by square footage
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?
- The second poll because it shows a higher percentage
- The first poll because larger sample sizes yield smaller margins of error (Correct answer)
- Both polls are equally reliable
- Neither poll is reliable without knowing the population size
Correct answer: The first poll because larger sample sizes yield smaller margins of error
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?
- Summer school significantly improves test scores
- There is no difference between the groups
- The difference is not statistically significant at the 0.05 level but may warrant further study (Correct answer)
- Summer school has a large practical effect on scores
Correct answer: The difference is not statistically significant at the 0.05 level but may warrant further study
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.
Question 6: A hospital records patient wait times over 30 days. The data is heavily right-skewed with outliers from mass-casualty events. Which measure best represents the typical patient wait time?
- Mean, because it uses all data points
- Median, because it is resistant to extreme outliers (Correct answer)
- Mode, because it shows the most common wait time
- Range, because it captures the full spread of the data
Correct answer: Median, because it is resistant to extreme outliers
The median is preferred over the mean for skewed distributions because it is not distorted by extreme values or outliers.
Question 7: A researcher conducts 20 separate hypothesis tests simultaneously at α=0.05 and finds 2 significant results. What is the primary statistical concern?
- The sample size is too small for 20 tests
- The familywise Type I error rate is inflated, increasing false-positive risk (Correct answer)
- Two significant results out of 20 is a strong finding
- A paired test should have been used instead
Correct answer: The familywise Type I error rate is inflated, increasing false-positive risk
Running multiple tests without correction inflates the probability of at least one false positive (familywise error); corrections like Bonferroni should be applied.
Statistics Case Studies & Practical Application 2
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?