Statistics – Final Exam Review – Chapters 1-3
1. Give an example that illustrates the difference between descriptive and inferential
statistics.
2. Identify the population and the sample: Thirty-eight nurses working in the San Francisco
area were surveyed concerning their opinions of managed health care.
3. Determine whether the following describe a parameter or a statistic:
a. In a survey of a sample of U.S. adults, 62% owned a portable cellular phone.
b. In a recent survey at the University of Arizona, 89 students were majoring in
astronomy.
4. Determine whether the following are qualitative or quantitative:
a. The Social Security numbers of the employees at an accounting firm.
b. The number of tax returns prepared by the employees at an accounting firm.
5. Give examples of the following levels of measurement:
a. nominal
b. ordinal
c. interval
d. ratio
6. Give examples of the following sampling techniques:
a. systematic
b. cluster
c. stratified
d. convenience
7. Determine the class width used in the frequency
distribution:
Minutes
5-9
10-14
15-19
20-24
e. random
Frequency, f
7
12
15
14
8. Sketch a dot plot where the minimum value is 5 and the maximum value is 12.
9. Find the mean, median, mode, midrange (average of max and min), range, standard deviation,
variance, and IQR of the following sample: 45, 83, 91, 72, 78, 85, 99, 85, 67, 88, 85, 90
10. The mean value of land and buildings per acre from a sample of farms is $1200, with a
standard deviation of $350. Use the Empirical Rule to find the percentage of farms with a
value of greater than $1550.
11. What is the meaning of the quartiles in a box-and-whisker plot?
12. The mean of the grades in a class is 78% with a standard deviation of 4.7%. Use z-scores
to determine which grades would be considered unusual and very unusual.
13. How do you determine a simple probability? What is the range of probability?
14. Give an example of mutually exclusive events and not mutually exclusive events.
15. The probability that a randomly selected person in Summit County skis is 0.62. What is the
probability that a randomly selected person does not ski?
16. Give examples of independent and dependent events.
17. Events A and B are mutually exclusive. P(A) = 0.13 and P(B) = 0.71. Find P(A or B).
18. A blood bank catalogs the types of blood, including positive or negative Rh-factor, given by
donors during the last five days. The number of donors who gave each blood type is shown in
the table. A donor is selected at random.
a. Find the probability that the donor has type O or type A blood.
b. Find the probability that the donor has type B blood or is Rh-negative.
c. Find the probability that the donor has type A blood given that they are Rh-positive.
Rh-factor
Positive
Negative
Total
O
156
28
184
Blood Type
A
B
AB
139
37
12
25
8
4
164
45
16
Total
344
65
409
19. In how many ways can the letters A, B, C, D, E, and F be arranged for a six-letter security
code?
20. There are four processes involved in assembling a certain product. These processes can be
performed in any order. Management wants to find which order is least time consuming.
How many different orders will have to be tested?
Statistics – Final Exam Review – Chapters 4-6
1. Give examples of discrete and continuous variables.
2. The number of cats per household in a small town is given:
Find the probability of randomly
Cats
0
1
selecting a household that has less
Households
1941 349
than 3 cats.
2
203
3
78
4
57
5
40
3. A sociologist surveyed households in a U.S. town. The random variable x represents the
number of dependent children in the households.
a. Determine the probability
x
0
1
2
3
4
5
6
distribution’s missing value.
P(x) 0.05 ?
0.23 0.21 0.17 0.11 0.08
b. Find the mean and standard
deviation.
c. Calculate the expected value.
4. A surgical technique is performed on seven patients. You are told there is a 70% chance of
success. Find the probability that the surgery is successful for
a. exactly five patients,
b. at least five patients, and
c. less than five patients.
5. Give examples of the following types of distributions:
a. binomial
b. geometric
c. Poisson
d. multinomial
6. The lengths of Atlantic croaker fish are normally distributed, with a mean of 10 inches and a
standard deviation of 2 inches. An Atlantic croaker fish is randomly selected.
a. Find the probability that the length of the fish is less than 7 inches.
b. Find the probability that the length of the fish is between 7 and 15 inches.
c. Find the probability that the length of the fish is more than 15 inches.
7. Find the z-score that has 78.5% of the distribution’s area to its right.
8. IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15.
Find the x-score that corresponds to a z-score of -1.57.
9. During a certain week the mean price of gasoline in California was   $2.029 per gallon. A
random sample of 38 gas stations is drawn from this population.
a. What is the probability that x , the mean price for the sample, was between $2.034
and $2.044? Assume   $0.049 .
b. What prices would be considered unusual?
10. Thirty-one percent of workers in the United States are college graduates. You randomly
select 50 workers and ask each if he or she is a college graduate. (Use the normal
distribution to approximate the binomial distribution.)
a. Find the probability that exactly 14 workers are college graduates.
b. Find the probability that at least 14 workers are college graduates.
c. Find the probability that fewer than 14 workers are college graduates.
11. Find the critical value z c necessary to form a confidence interval at the 85% confidence
level.
12. Find the value of E, the margin of error, for c = 0.99, s = 3.0, and n = 6.
13. Construct a 90% confidence interval for the population mean  . Assume the population has
a normal distribution. From a random sample of 36 days in a recent year, the closing
stock prices for Hasbro has a mean of $19.31 and a standard deviation of $2.37.
(Interactive Data Corp.)
14. Construct a 95% confidence interval for the population mean  . Assume the population has
a normal distribution. In a random sample of seven computers, the mean repair cost was
$100.00 and the standard deviation was $42.50.
15. In a survey of 350 people who microwave often, 55% of these people were in-favor of food
irradiation to kill disease microbes. Construct a 99% confidence interval for the
proportion of frequent microwave users who favor irradiation.
Statistics – Final Exam Review – Chapters 7,9, and 10
1. Decide whether each confidence interval indicates that you should reject H 0 . H 0 :   54 .
a.
54.5,55.5
b.
51.5,54.5
c.
53.5,56.5
2. Given H 0 :   8.5 , H a :   8.5 , and P  0.0691 .
a. Do you reject or fail to reject H 0 at the 0.05 level of significance?
b. Do you reject or fail to reject H 0 at the 0.10 level of significance?
3. An automotive battery manufacturer guarantees that the mean reserve capacity of a certain
battery is greater than 1.5 hours. To test this claim, you randomly select a sample of 50
batteries and find the mean reserve capacity to be 1.55 hours with a standard deviation
of 0.32 hour. At   0.10 , do you have enough evidence to support the manufacturer’s
claim?
4. A coffee shop claims that its fresh-brewed drinks have a mean caffeine content of
80 mg/5 oz. You work for a city health agency and are asked to test this claim. You find
that a random sample of 42 five-ounce servings has a mean caffeine content of 83 mg and
a standard deviation of 35 mg. At   0.05 , do you have enough evidence to reject the
shop’s claim?
5. A weight loss program claims that program participants have a mean weight loss of at least
10 pounds after one month. You work for a medical association and are asked to test this
claim. A random sample of 30 program participants and their weight losses ( in pounds)
after one month is listed below. At   0.03 , do you have enough evidence to reject the
program’s claim?
5.7, 5.7, 6.6, 6.7, 7.0, 7.1, 7.9, 8.2, 8.2, 8.7, 8.9, 9.0, 9.3, 9.5, 9.6, 9.8,
10.2, 10.5, 10.6, 10.6, 11.1, 11.2, 11.5, 11.7, 11.8, 12.0, 12.7, 12.8, 13.8, 15.0
6. A computer repairer believes that the mean repair cost for damaged computers is more than
$95. To test this claim, you determine the repair costs for seven randomly selected
computers and find that the mean repair cost is $100 per computer with a standard
deviation of $42.50. At   0.01 , do you have enough evidence to support the repairer’s
claim? (Consumer Reports)
7. A medical researcher estimates that no more than 55% of U.S. adults eat breakfast every
day. In a random sample of 250 U.S. adults, 56.4% say the eat breakfast every day. At
  0.01, is there enough evidence to reject the researcher’s claim. (U.S. National Center
for Health Statistics)
8. A doctor says the standard deviation of the lengths of stays for patients involved in a crash
in which the vehicle struck a tree is 6.14 days. A random sample of 20 lengths of stay of
patients involved in this type of crash has a standard deviation of 6.5 days. At
  0.05 , can you reject the doctor’s claim? (National Highway Traffic Safety Admin.)
9. The ages (in years) of 11 children and the number of words in their vocabulary are given:
Age
Vocab
1
3
a.
b.
c.
d.
e.
f.
2
440
3
1200
4
1500
5
2100
6
2600
3
1100
5
2000
2
500
4
1525
6
2500
Display the data in a scatter plot.
Calculate the correlation coefficient.
Make a conclusion about the type of correlation.
Is the correlation significant at the   0.01 level?
Find the equation of the regression line.
Use the equation of the regression line to predict the vocabulary of a 3 12 year old.
10. The distribution of the time of day of roadside hazard
crash deaths for a previous year is 34% - midnight
to 6 am, 15% - 6 am to noon, 22% - noon to 6 pm, and
29% - 6 pm to midnight. The results of a recent
study of 627 randomly selected hazard crash deaths
are shown in the table. At   0.01, has the
distribution changed?
Frequency, f
Time of Day
Midnight to 6 am
224
6 am to Noon
128
Noon to 6 pm
115
6 pm to Midnight
160