Chapter 7 Worksheet
Name_________________________
T-tests/intervals
1. A publisher wants to determine the list price for a new algebra book. A survey of the list price
of eight competing books sold by other companies showed an average price of $39.95 with a
standard deviation of $2.85. Construct a 95% confidence interval for the average list price for a
new algebra book.
2. A survey of 11 randomly selected city dwellers found that they were wasting an average of
57 gallons of water per day. The standard deviation was 6.9 gallons per day. Construct a 90%
confidence interval for the average amount of water wasted daily by those people.
3. The EPA reports that 17% of Americans recycled garbage in 1990. One survey of ten
randomly selected Americans indicated that they generated 5.7, 6.3, 2.9, 4.2, 5.3, 2.7, 3.6, 3.4,
3.9, and 4.5 pounds of garbage per day. Construct a 90% confidence interval for the average
number of pounds of garbage generated per day.
4. According to Backpacker, people visit Glacier National Park for peace and quiet. The noise
level in (decibels) at eight different locations in the park produced the following readings: 14,
28, 23, 29, 19, 25, 22, 17. Find a 95% confidence interval for the average noise level.
5. A college claims that its computer science graduates can expect an average starting salary of
$24, 800 annually. Sixteen graduates of that college had an average starting salary of $24,000
with a standard deviation of $1850. At a 5% level, can we conclude that the average starting
salary is significantly less than $24, 800?
6. The New York City Taxi and Limousine Commission claims that the average fare for a taxi ride
from JFK airport to Manhattan is $26.20. A random sample of nine trips from the airport to
Manhattan had an average fare of $28.15 with a standard deviation of $1.09. At a 5% level of
significance, can we conclude that the average fare for a taxi ride from JFK to Manhattan is
more than $26.20?
7. City officials in Roxville claim that a call to the 911 police emergency number will bring an
ambulance in an average of 4.8 minutes. Officials of the EMS claim that ambulance response
time has improved since the instillation of a new computer system. In a random sample of ten
calls for an ambulance, the average response time was 4.6 minutes with a standard deviation of
1.2 minutes. At a 1% level, does this indicate an improvement of service?
8. The three leading manufacturers of peanut butter claim that a typical three-tablespoon
serving of peanut butter contains about 24 grams of fat and 285 calories. To check on the
accuracy of this claim, a random survey of 18 three-tablespoon servings of peanut butter is
taken. The sample results in an average of 288 calories per three-tablespoon serving with a
standard deviation of 5 calories. Using a 5% level of significance, test the null hypothesis that
the mean calorie content for the sample is the same as the calorie content claimed by the
manufacturer.
9. Ten members of a health club kept the number of hours each spends per week at the club.
Their hours were 10, 8, 3, 2, 12, 3, 11, 14, 7, and 5 hours. Construct a 90% confidence interval
for the average amount of time spent by a member at the health club.
10. The kidneys of a human body normally remove toxic wastes from the blood. When a
person’s kidneys deteriorate, the person must be treated by dialysis, which is a procedure
whereby the toxic removal procedure is performed artificially by a machine. However, it is
known that dialysis can result in retention of phosphorous in the blood. This condition must be
monitored carefully. The phosphorous levels of nine dialysis patients were measured, and the
following results were obtained: 4.7, 5.3, 5.9, 4.9, 5.1, 6.2, 5.8, 5.5, 6.4. Assuming that the
phosphorous levels of dialysis patients are normally distributed, construct a 90% confidence
interval for the average level of phosphorous in the blood of dialysis patients.
11. Health officials tested the air at seven tunnels to determine the pollution content. The
officials found an average of 18 ppm of a certain pollutant in the air at these tunnels. The
standard deviation was 3.2 ppm. Find a 95% confidence interval for the average ppm content of
this pollutant in the air at these tunnels.
12. Medicare officials claim that a typical beneficiary nationwide uses an average of 57 days of
skilled nursing care in any calendar year. A random survey of 12 skilled-care nursing facilities in
the Northeast found that they provided an average of 52 days of skilled nursing care in any
calendar year. The standard deviation was 12 days. Using a 5% level of significance, test the null
hypothesis that the national average is less than 57 days of skilled nursing care in any calendar
year.
13. Many nursing homes and rehabilitation companies charge exorbitant prices for services
rendered. In 1995, nursing homes charged an average of $54 for 15 minutes of speech therapy.
Nursing homes deny this. A random survey of 14 nursing homes found that they charge an
average of $56 for 15 minutes of speech therapy. The standard deviation was $3. Using a 5%
level of significance, test the null hypothesis that the average charge for 15 minutes of speech
therapy is $54.
14. An airline company is about to order some inflatable rubber life rafts for emergency use on
its planes. Six samples of life rafts produced by one company needed an average of 7 seconds
to be fully inflated. The standard deviation was 1.86 seconds. Five samples of life rafts
produced by a second company needed an average of 6 seconds to be fully inflated. The
standard deviation was 2.13 seconds. Using a 5% level of significance, is the difference between
the mean time required to fully inflate the life rafts produced by the two companies significant?
15. Ten patients at Brooks Hospital required an average stay of 5 days after a particular surgical
procedure. The standard deviation was 1.35 days. Eight patients at Mercy Hospital required an
average of 6.5 days after the same surgical procedure. The standard deviation was 1.98 days.
Using a 5% level of significance, is there any significant difference between the average length
of stay at both hospitals after the surgical procedure?
16. The typical credit card holder charges $2750 a year and pays, on average, $315 in interest
charges. One research group randomly selected 12 credit card holders and found that they
charged an average of $3270 per year. The standard deviation was $476. A second research
group surveyed 14 credit card holders and found that these credit card holders charged an
average of $3064 per year. The standard deviation was $716. Using a 5% level of significance, is
there any significant difference between the average charge as reported by these two research
groups?