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## Example Questions

### Example Question #1 : How To Find Confidence Intervals For A Difference Between Unpaired Means

The 95% confidence interval created for the difference in means between two training programs for middle distance college runners is . The variable being measured is the improvement in seconds of mile times over the course of a season. One program has more speed work and intervals, while the other focuses more on distance training.

What does the confidence interval tell us about the difference in the two programs?

**Possible Answers:**

Zero is not in the interval, so reject the null. This is evidence that one program is significantly better at reducing mile times.

The mean improvement of second is too small to matter, so reject the null. There is no evidence that one program is better at reducing miles times.

Zero is in the interval, so do not reject the null. There is no evidence that one program is better than the other.

is greater than , so reject the null. This is evidence that one program is better at reducing mile times than the other.

The confidence interval is large, so one program is clearly better at reducing mile times than the other.

**Correct answer:**

Zero is in the interval, so do not reject the null. There is no evidence that one program is better than the other.

For there to be a statistically significant difference in the training programs, the 95% confidence interval cannot include zero. includes zero, so we can't say that one program is significantly better than the other.

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