Name the Inference Procedure
1. The football coach randomly selected ten players and timed how long each player took to perform a certain
drill. The times (in minutes) were:
6.9
8.2
7.0
11.6 7.0
6.2
10.6 10.7 8.9
13.8
Estimate the mean time for all players.
2. Is the mean lifetime of particular type of car engine greater than 220,000 miles? To test this claim, a random
sample of 40 engines is measured, yielding an average of 226,450 miles and a standard deviation of 11,500
miles.
3. A teacher is interested in whether there is a difference between the mean math score of the girls and the
mean math score of the boys. She randomly selects 10 girls from the class and then randomly selects 10 boys.
4. At one SAT test site students taking the test for a second time volunteered to inhale supplemental oxygen for
10 minutes before the test. In fact, some received oxygen, but others (randomly assigned) were given just
normal air. Test results showed that 42 of 66 students who breathed oxygen improved their SAT scores,
compared to only 35 of 63 students who did not get the oxygen. Is there is evidence that breathing extra
oxygen can help test-takers think more clearly?
5. A researcher was interested in comparing the salaries of female and male
employees of a particular company. Independent random samples of 8 female
employees (sample 1) and 15 male employees (sample 2) yielded the following
weekly salaries (in dollars). Do the data provide sufficient evidence to conclude that
the women at this company make less than men at the company?
6. A laboratory tested thirty randomly-selected chicken eggs and found that the mean amount of cholesterol
was 223 milligrams with standard deviation of 10.2 milligrams. Estimate the true mean cholesterol content of
all such eggs.
7. A father is concerned that his teenage son is watching too much television each day, since his son watches an
average of 2 hours per day. His son says that his TV habits are no different than those of his friends. Since this
father has taken a stats class, he knows that he can actually test to see whether or not his son is watching
more TV than his peers. The father collects a random sample of television watching times from boys at his
son's high school and gets the following data:
1.9
2.3
2.2
1.9
1.6
2.6
1.4
2.0
2.0
2.2
Is the father right? That is, is there evidence that other boys average less than 2 hours of television per day?
8. A fitness trainer wants to know if her weight-lifting program can quickly improve upper body strength in older
people. To find out, she has a group of randomly selected people over 55 years old do push-ups for 90
seconds and counts the number each can do. After these people participate in her weightlifting program for 3
weeks, she tests them again in the same way. The results are below. Does the program help?
9. Are female or male students more likely to attend college outside their home state? In order to find out,
random samples of male and female college-bound high school seniors were taken in the Dallas/Fort Worth
metropolitan area. In September following their high school graduations, the students in the samples were
contacted to see if they were attending college in Texas or outside of it. (Students who were not attending
college were eliminated from the study.) The results are summarized in the following table. Does the data
indicate that there is a difference in out-of-state attendance rates of male and female students in Texas?
10. A researcher was interested in comparing the heights of women in two different
countries. Independent random samples of 9 women from country A and 9 women
from country B yielded the following heights (in inches). Determine a 90%
confidence interval for the difference between the mean height of women in
country A and the mean height of women in country B.
11. Based on information from State Farm Insurance Company, 67% of all damage liability claims are made by
single people under the age of 25. A random sample of 53 claims in Collin County showed 42 claims were
made by single people under the age of 25. Does this indicate that the percent of insurance claims by single
people under the age of 25 in Collin County is higher than the national percent?
12. In a random sample of 250 high school students, it was found that 84% of them later graduated. Estimate the
true proportion of all high school students who graduate.
13. The following information is taken from the U.S. Department of Commerce Environmental Data Service.
Below is the average temperature (in Fahrenheit) for Buffalo, New York and Grand Rapids, Michigan. Do these
data indicate that there is a difference in average temperatures?
The following are not inference procedures, but are from Chapter 9 (Sampling Distributions). How would you
solve?
14. According to government data, 22% of American children under the age of 6 live in households with incomes
less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children.
What is the probability that less than 20% of the sample are from poverty households?
15. At Morristown Memorial Hospital, weights of newborns are normally distributed with a mean of 110 ounces
and a standard deviation of 15 ounces. What is the probability that a random sample of ten newborns has a
mean birthweight under 105 ounces?