Confidence Intervals for Means
Name_____________________
1. In Roosevelt National Forest, the rangers took random samples of live aspen trees and measured the base
circumference of each tree. The first sample had 30 trees with a mean circumference of 15.71 inches and a
population standard deviation of 4.63 inches. Find and interpret a 95% confidence interval for the mean
circumference of aspen trees from these data.
2. A special feature of camping in the western United States is listening to coyotes howl at night. Just how long in one
coyote howl? Since coyotes tend to hunt in groups, it can seem that howls go on for a long time. Based on a
random sample of 102 coyotes, it was found that the mean duration of the howl was 1.2 seconds with a sample
standard deviation of 0.4 seconds. Compute and interpret a 99% confidence interval for the population mean
duration of all coyote howls.
3. How long does it take to fall asleep at night? This depends on what happened the night before. A random sample
of 38 college students was kept awake all night and the next day (24 hours). The mean time for this group to go to
sleep the next night was 2.5 minutes with standard deviation of 0.7 minutes. Compute and interpret a 90%
confidence interval for the mean time of all such students to fall asleep.
4. Test plots in Yellowstone National Park were used to study tree reproduction of lodgepole pine. In plots of 50
square meters, the number of new lodgepole saplings was counted. In a given region, based on long observation,
the standard deviation is estimated at 44. How many 50-square-meter plots should be used in such a region to be
95%sure the sample mean of lodgepole saplings is within 10 saplings of the population mean?
5. Root depth for grasses and shrubs in a type of soil known as glacial outwash was studied in Yellowstone and the
standard deviation was found to be approximately 8.94 inches. In a proposed study region of glacial outwash, how
many plants should be carefully dug up and studied to be 90% sure that the sample mean root depth is within 0.5
inches of the population mean root depth?
6. A random sample of 37 adult male desert bighorn sheep indicated the standard deviation of the sheep weights to be
15.8 pounds. How many more such adult male desert bighorn sheep should be included in the sample to be 90%
sure that the sample mean weight is within 2.5 pounds of the population mean weight of all such bighorn sheep in
this region?
7. How many calories are there in 3 ounces of French fries ? It depends on where you get them. Good Cholesterol
Bad Cholesterol, by Roth and Streicher, gives the data from eight popular fast-food restaurants. The data are
shown below. Construct and interpret a 99% confidence interval for the mean calorie count in 3 ounces of French
fries obtained from fast-food restaurants.
222
249
255
222
254
237
230
287
8. A random sample of 12 East Coast college and universities gave the following percentage tuition increases for a 2year period. Compute a 90% confidence interval for the population mean percentage tuition increase of all East
Coast colleges and universities.
3.9
6.7
2.3
6.6
3.7
4.6
9.4
4.3
4.8
3.1
3.9
3.1
9. The following information fives age in years and was obtained from The Sport Encyclopedia, Pro Football (11th
Eition). Compute an 85% confidence interval for the population mean age of all professional football players.
26
32
29
22
32
24
27
33
24
25
25
32
25
23
22
36
23
32
33
28
26
24
24
32
25
32
29
25
31
29
31
30
28
26
25
34
30
22
28
27