Confidence Intervals – 2 sample Means
Name_____________________
1. A group of 12 companies in the insurance industry has a mean annual profit as percent of revenue of 4.4 with
a standard deviation of 1.6 while the mean annual profit as a percent of revenue for a group of 10 health
care companies was 4.6 with a standard deviation of 1.4. Find a 90% confidence interval for the difference
in mean annual profit. At the 90% level of confidence, does it appear that one industry group has a higher
profit as a percentage of revenue?
2. A random sample of 45 professional football players indicated the mean height to be 6.18 feet with a sample
standard deviation of 0.37 feet. A random sample of 40 professional basketball players indicated the mean
height to be 6.45 feet with a standard deviation of 0.31 feet. Find a 95% confidence interval for the
difference in mean heights of professional football and basketball players. Does it appear that the average
height of football players tends to be shorter than the average height of basketball players?
3. The Fleetfoot Shoe Company claims that the average yearly salary of its workers is $29,800. The union
believes that the average salary is much less. A random sample of 64 employees shows their average salary
to be $29,000 with a standard deviation of $800. Use a 5% level of significance to determine whether the
magazine should be continued.
4. A random sample of 43 eastern colleges hand an average percentage of salary increase for professors of 3.6
with a standard deviation of 1.8. Another random sample of 40 western colleges gave the average
percentage of salary increases of professor as 3.3 with a standard deviation of 1.7. Compute a 90%
confidence interval for the average difference in percent of salary increase between the eastern and
western colleges. Does it appear that the average percentage salary increase for eastern college professors
is higher than that for western college professors?
5. A random sample of 18 adult male wolves from the Canadian Northwest Territories gave an average weight of
98 pounds with standard deviation of 6.5 pound. Another sample of 24 adult male wolves from Alaska gave
an average weight of 90 pounds with a standard deviation of 7.3 pounds. Find a 85% confidence interval for
the difference in mean weight of the Canadian and Alaskan wolves. Does it appear that the average weight
of the adult male wolves from Canada is greater than that of the Alaskan wolves?
6. A sociologist is studying the size of rural Canadian families. The number of children in each family is noted
for low-income families and high-income families. Compute a 95% confidence interval for the difference in
mean number of children from low- and high-income families. Does there seem to be a difference in the
average number of children low- or high-income families?
Low Income
High Income
5
3
7
1
9
6
3
5
3
5
4
3
4
0
4
2
2
4
4
1
6
10
1
10
8
3
6
7
4
5
7. A reading test was administered to both a control group and an experimental group after 6 weeks of
instruction during which the experimental group received peer tutoring and the control group did not. The
average score for the 30 subjects in the control group of the vocabulary portion of the test was 349.2 with
standard deviation of 56.6. For the experimental group of 30 children, the mean score on the same portion
of the test was 368.4 with standard deviation 39.5. use a 1% level of significance to test the claim that the
experimental group performed better than the control group.
8. How long do patients stay. Find a 99% confidence interval for the population average number of days
patients spend in the hospital.
7.2
7.3
7.9
6.8
7
7.1
6.9
6.8
9.9
7.3
7.5
6.9
6.6
6.8
7.3