APFIVE Sample Size and Confidence Interval Width
Which of the following is true regarding the change in the 95% confidence interval for the mean gas mileage when the sample size increases from 10 to 20, while the sample mean and standard deviation remain the same?
| Sample Scenario | Sample Size | Confidence Interval (mpg) |
|---|---|---|
| Original Sample (n=10) | 10 | (25.91, 28.49) |
| Increased Sample (n=20) | 20 | (26.36, 28.04) |
A
The confidence interval becomes narrower, indicating a more precise estimate of the true mean.
B
The confidence interval remains unchanged because the sample mean and standard deviation have not changed.
C
The confidence interval becomes wider due to increased variability from the larger sample.
D
A larger sample size increases the degrees of freedom so much that the confidence interval loses validity.
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