485 / 762
Chapter 11: Confidence Intervals – Large Samples
485
Example 11-7:
The Student President of a large regional university wishes
to estimate the average distance commuting students’ travel to the campus.
A sample of 49 students was randomly selected and yielded a mean of 42
miles and a standard deviation of 7 miles. Construct a 99% confidence
interval estimate for the true mean distance commuting students travel to the
campus. Assume that the population of commuting distances by the students
is normally distributed.
Solution:
Given
= 0.01,
⁄
= 2.5758,
̅
= 42,
= 49,
= 7, and
̅
√
= 1.0. Thus the 99% confidence interval estimate for the mean
distance, using the formula, is 42
2.5758
1.0 = 42
2.5758. That is, we
are 99% confident that the average distance commuting students travel to the
campus will lie between 39.4242 miles and 44.5758 miles.
Again, we can use the
Large Sample Confidence Interval for a Single
Population Mean
workbook to help with the computations. However we
will have to use the portion of the workbook which assumes that the
population standard deviation is unknown.
Figure 11- 11
shows the output
with the 99% confidence interval. Observe that the 99% confidence interval
is the same as the interval computed by the formula.