Sample Size and Confidence Interval Width
The table shows two 95% confidence intervals for the mean gas mileage of a vehicle, calculated from samples of size n=10 and n=20. The sample mean and standard deviation were the same for both calculations. Which statement best explains the change in the confidence interval when the sample size was increased?
| Sample Size | 95% Confidence Interval (mpg) |
|---|---|
| n = 10 | (25.91, 28.49) |
| n = 20 | (26.36, 28.04) |
A
The confidence interval remains unchanged because the sample mean and standard deviation have not changed.
B
The confidence interval becomes narrower, indicating a more precise estimate of the true mean.
C
A larger sample size increases the degrees of freedom so much that the confidence interval loses validity.
D
The confidence interval becomes wider due to increased variability from the larger sample.
Question Leaderboard
Not enough data yet to show leaderboard.