FINAL EXAMINATION
FOR INSTRUCTORS USE
1. a......./3 b....../3 c......./3 d......./6 ........../15
2. ........../7
3. ........../5
4. ........../5
5. ........../5
6. ........../5
7 a......./4 b....../5 c......./5 ........../14
8. a......./6 b....../6 ........../12
9. a......./6 b....../6 ........../12
10. a......./5 b....../5 ........../10
11. ........../10
TOTAL ........../100
| 1. The following data are based on the results of a
survey to examine television viewing preferences.
|
| White | ||||
| Black | ||||
| Spanish-speaking | ||||
| Other |
Source: Harold W. Stanley and
Richard G. Niemi, Vital statistics on American Politics,
3rd ed., 1992, p.54
| If one viewer is selected at random, find the probability that |
| a. viewer prefers "Cable" |
| b. viewer prefers "CNN" or "Spanish-speaking" |
| c. Viewer prefers "CNN" given that she/he is "black" |
| d. Are the events "prefer Early News" and
" being white" independent? Are they mutually
exclusive? Justify your answer.
|
| 2. The accompanying figure is a representation of a
system comprised of three subsystems. Subsystem A and C has two
components that operate in series, and subsystem B has one component. The
probability of failure for each component in the subsystem A and B is .2,
and in the subsystem C is .1. Assume the components operate independently
of each other.
|
|
| Find the probability that
the system operates properly. |
| 2. A judge is 65% sure that a suspect has committed
a crime. During the course of the trial a witness convinces the judge
that there is an 85% chance that the criminal is left-handed. If 23% of
the population is left handed and the suspect is also left-handed, with
this information, how certain should the judge be of the guilt of the
suspect?
|
| 3. Dave and Rick are training for the Boston
Marathon. Dave is training on a course in Cumberland, while Rick is
training on a course in Frostburg. The mean time to complete the
Cumberland course is 167.4 minutes, and the standard deviation is 25.9
minutes. The mean time to complete the Frostburg course is 143.1 minutes,
and the standard deviation is 20.7 minutes. Dave says his course time on
the Cumberland course is 91.5 minutes, and Rick says his course time on
the Frostburg course is 86.2 minutes. Who do you think will do better in
the Boston Marathon? Justify your answer.
|
| 4. The board of examiners that administered the real estate brokers' examination in a certain state found that the mean score on the test was 435 and the standard deviation was 72. If the board wants to set the passing score so that only the best 30% of all applicants pass. what is the passing score? Assume that the scores are normally distributed. |
| 5. In Japan number of earthquakes in a week has a
Poisson distribution with mean 0.3. What is the probability that there
will be at least one earthquake in Japan within the next week.
|
| 6. Fifty percent of all 1988 domestic cars were equipped with power windows (Ward's Automotive Yearbook). Suppose a driver encounters 5 1988 domestic cars on her next trip to the work. Find the probability that at least 1 will have power windows. |
| 7. A taxi service based at an airport can be characterized as a transportation system with one source terminal and a fleet of vehicles that take passengers from the terminal to different designations. Each vehicle returns to the terminal after some random trip time and makes another trip. To improve the vehicle-dispatching decisions involved in such system, Sims and Templeton (1985) assumed travel times of successive trips are independent exponential random variables to model the system. Assume q = 20 minutes. |
| a. What is the mean trip time for the taxi service? |
| b. What is the probability that a particular trip will take between 10 to 15 minutes. |
| c. Two taxis have just been dispatched. What is the
probability that both will be gone for more than 30 minutes?
|
| 7. Insurance claims indicate that the average charge by an obstetrician in a certain large northeastern city during 1991 for a Cesarean section delivery was $3900 with a standard deviation of $525. |
| a. Find the probability that a randomly selected obstetrician will charge more than $5000 for a Cesarean section delivery. |
| b. A random sample of 36 obstetricians from this city is taken. What is the probability that the average charge by these doctors will be more than $4100? |
| c. Suppose that you got information on the cost of
two Cesarean section deliveries. What is the probability that in both
cases the obstetricians charged more than $5000.
|
| 8. Pulse rate is an important measure of the fitness of a person's cardiovascular system. The mean pulse rate for all U.S. adults is approximately 72 heart beats per minute. A random sample of 21 U.S. adults who jog at least 15 miles per week had a mean pulse rate of 52.6 beats per minute. Assume that the population standard deviation is 3.22 beats per minute. |
| a. Find a 95% confidence interval for the mean pulse rate of all U.S. adults who jog at least 15 miles per week. |
| b. What should be the sample size to estimate mean
pulse rate of U.S. adults who jog at least 15 miles per day to within
1.00 beats per minute with 95% confidence.
|
| 9. The Journal of Fish Biology (August, 1990) reported on a study to compare the incidence of parasites (tapeworms) in species of Mediterranean and Atlantic fish. In the Mediterranean Sea, 599 brill were captured and dissected, and 211 were found to be infected by the parasite. In the Atlantic Ocean, 123 brill were captured and dissected, and 26 were found to be infected. |
| a. Compare the proportions of infected brill at the two capture sites using a 90% confidence interval. |
| b. Does this result provide sufficient evidence to
indicate that the proportions of infected brill for the Mediterranean Sea
and Atlantic Ocean are different? Test at a=0.05.
|
| 10. Shorkey, McRoy, and Armendariz examined the
relationship between the intensity of parental punishment practices and
various demographic characteristics of mothers. The intensity score
summary statistics are shown in the accompanying table, with higher
scores showing a greater intensity of parental punishments.
|
| Single mothers | |||
| Separated mothers |
| a. Is there a significant evidence that the mean intensity of parental punishment scores for single mothers is different than the mean intensity scores for separated mothers? State the null and alternative hypotheses, give the P-value. What is your conclusion? |
| b. Use a 95% confidence interval to estimate the
difference between the mean intensity of parental punishment scores for
single and separated mothers.
|
| 11. Patricia Ostrow and colleagues conducted a study
of 193 acute care patients in 6 Midwestern hospitals ("Functional
Outcomes and Rehabilitation: An Acute Care Field Study," Journal
of Rehabilitation Research and Development, Summer, 1989). One
hundred and thirty-two patients received occupational therapy services
because of requests from the referring physicians, while the other 61 did
not receive such services. All patients were classified according to the
severity of disability. The following table gives the data.
|
| Received Occupational Therapy? |
| ||
| Yes | |||
| No | |||
| Conduct a test to
determine whether severity of disability and receiving occupational
therapy are dependent factors. Test using a=0.05.
|