APFIVE Confidence Interval for Difference in Means
The table below provides summary statistics for the number of accidents per month in two departments, based on independent samples. Which of the following correctly describes a 95% confidence interval for the difference in the mean number of accidents per month (First Department - Second Department)?
Department Accident Data:
| Department | Mean Accidents | Standard Deviation | Sample Size (n) |
|---|---|---|---|
| First Department | 12.3 | 3.5 | 30 |
| Second Department | 7.6 | 3.4 | 30 |
A
Calculating an interval using a z-interval that ignores the distinct sample sizes.
B
Applying a paired data methodology to the two independent samples.
C
Constructing separate confidence intervals for each department and then subtracting the endpoints.
D
Using the data provided, the 95% confidence interval for the difference (first minus second) is approximately $$ (2.92, 6.48)$$.
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