Statistics Case Studies & Practical Application 4

Question 1

A researcher reports: 'The 95% confidence interval for the mean recovery time is (12.4 days, 15.6 days).' What is the correct interpretation?

Accepted Answer

If the study were repeated many times, 95% of such intervals would capture the true mean

Answer

A 95% CI means that the procedure, repeated across many samples, would produce intervals containing the true parameter 95% of the time; it is not a probability statement about one interval.

Question 2

An HR analyst runs a multiple regression predicting employee performance from age, tenure, and training hours. The VIF for tenure is 8.7. What does this indicate?

Accepted Answer

Tenure is highly correlated with other predictors, indicating multicollinearity

Answer

A VIF above 5-10 signals multicollinearity, meaning tenure is strongly correlated with other predictors, which inflates coefficient standard errors.

Question 3

A school wants to estimate the proportion of students who walk to school. They survey 200 students and find 80 walk. What is the 95% confidence interval for the true proportion?

Accepted Answer

(0.33, 0.47)

Answer

With p̂=0.40 and n=200, the margin of error is 1.96×√(0.40×0.60/200)≈0.068, giving the interval (0.332, 0.468) ≈ (0.33, 0.47).

Question 4

A public health study finds that counties with more fast-food restaurants have higher obesity rates (r=0.71). A reporter headlines: 'Fast Food Causes Obesity.' Why is this misleading?

Accepted Answer

Ecological correlations (county-level data) cannot support causal claims about individuals

Answer

Using aggregate data to make individual-level causal claims commits the ecological fallacy; county-level correlations don't establish causation for individuals.

Question 5

A company surveys employee satisfaction on a 1-5 Likert scale. Management wants to compare average satisfaction between departments using a t-test. What assumption concern is most relevant?

Accepted Answer

Likert data is ordinal, and using means may be inappropriate; normality should be verified

Answer

Likert data is technically ordinal, and treating it as interval-level for t-tests is debated; checking for approximate normality or using nonparametric alternatives is advisable.

Statistics Practice Test

Statistics Practice Test

Statistics Case Studies & Practical Application 4