Final Exam Fall 2013

Math 110
Fall 2013
Name ______________________
Final Exam
Remember: Write down the formula from the outline if used!
1. The paper “I Smoke But I am not a Smoker” (Journal of American College Health
[2010]) describes a survey of 899 college students who were asked about their
smoking behavior. Of the students surveyed, 268 classified themselves as
nonsmokers, but said yes when asked later in the survey if they smoked. These
students were classified as “phantom smokers”, meaning that they did not view
themselves as smokers even though they do smoke at times. The authors were
interested in using these data to determine if there is convincing evidence that
more than 25% of college students fall into the phantom smoker category. Test
the author’s claim at a 5% significance level.
1
2. Thirty percent of all automobiles undergoing an emissions inspection at a certain
inspection station fail the inspection.
a) Among 15 randomly selected cars, what is the probability that 5 fail the
inspection?
b) Among 15 randomly selected cars, find the mean and the standard deviation
of the number of cars that fail the inspection.
c) Would it be unusual to find that 10 of the 15 cars would fail the inspection?
Why or why not?
3. The Internet is affecting us al in many different ways, so there are many reasons
for estimating the proportion of adults who use it. Assume that the manager of EBay wants to determine the current percentage of U. S. adults who now use the
Internet. How many people must be surveyed in order to be 95% confident that
the sample percentage is within 3 percentage points?
2
4. Many people believe that criminals who pear guilty tend to get lighter sentences
than those who are convicted in trials. The accompanying table summarizes
randomly selected sample data for San Francisco defendants in burglary cases.
All of the subjects had prior prison sentences.
Guilty Plea
Not Guilty Plea
Sent to Prison
392
58
Not Sent to Prison
564
14
If one person is randomly selected, find each of the following.
a) Find the probability that the person pled guilty.
b) Find the probability that the person was sent to prison.
c) Find the probability that the person pled guilty and was sent to prison.
d) Find the probability that the person pled guilty or was sent to prison.
e) Find the probability that the person pled guilty given that the person was sent
to prison.
f) Find the probability that the person was sent to prison given that the person
pled guilty.
g) Are the events “pleading guilty” and “being sent to prison” mutually excusivie
events? Why or why not?
h) Was the data collected qualitative or quantitative?
3
i) Use a 5% significance level to test the claim that the sentence (being sent to
prison or not) is independent of the plea.
j) If you were an attorney defending a guilty defendant would these results
suggest that you should encourage a guilty plea?
k) Construct a 95% confidence interval for the proportion of defendants who
plead guilty and went to prison.
4
5. A company sent seven of its employees to attend a course in building selfconfidence. These employees were evaluated for their self-confidence before and
after attending this course. The following table gives the scores (on a scale of 1 to
15, 1 being the lowest and 15 being the highest) of these employees before and
after they attended the course.
Before
After
8
10
5
8
4
5
9
11
6
6
9
7
5
9
Test at the 1% significance level whether attending this course increases the mean
score of employees.
5
6. In a 1993 survey of 560 college students, 171 said that they used illegal drugs
during the previous year. In a recent survey of 720 college student, 263 said that
they used illegal drugs during the previous year. Use a 5% significance level to
test the claim that the proportion of college students using illegal drugs in 1993
was less than it is now.
6
7. Assume that heights of men are normally distributed with a mean of 69.0 inches
and a standard deviation of 2.8 inches.
a) A day bed is 72 inches long. What is the probability that a randomly selected
man’s height will exceed the length of the day bed?
b) In designing a new bed, you want the height of the bed to equal or exceed the
height of at least 95% of all men. What is the minimum length of the bed?
8. Listed below are annual salaries (in thousands of dollars) for a simple random
sample of NCAA Division 1-A head football coaches.
235
159
492
530
138
125
128
900
360
212
a) Is the data collected qualitative or quantitative?
b) Find the mean, median, standard deviation and variance for the above data.
c) Are there any unusual data above? Why or why not?
d) Which average would you use for this data? Why or why not?
e) Would you describe the data above as discrete or continuous? Why?
7
f) Construct a 95% confidence for the population mean salaries.
9. Identify the level of measurement as nominal, ordinal, discrete or continuous.
a) The eye colors of all fellow students in your statistics class
b) The pulse rates of students in your statistics class as they are taking this exam
c) A movie’ critics rating of “must see, recommended, not recommended, don’t
even think about going”
d) The actual temperatures in degrees Fahrenheit of the rooms in this building
during final exams
e) The number on the back of a football uniform
f) The number of students who pass their final exams today
10. Seventy-two percent of Americans squeeze their toothpaste from the top. This
and other not-so-serious findings are included in The First Really Important
Survey of American Habits. Those results are based on 7000 responses from the
25000 questionnaires that were mailed.
a) Is the 72% a statistic or a parameter? Explain.
b) Does the survey constitute an observational study or an experiment?
8
11. For women aged 18 – 24, systolic blood pressure (in mm Hg) are normally
distributed with a mean of 114.8 and a standard deviation of 13.1. Hypertension
is commonly defined as systolic blood pressure above 140.
a) If a woman between the ages of 18 - 24 is randomly selected, find the
probability that her systolic blood pressure is greater than 140.
b) If 4 women in that age bracket are randomly selected, find the probability that
their mean systolic blood pressure is greater than 140.
c) Given that part (b) involves a sample size that is not larger than 30 why can
the Central Limit Theorem be used?
d) If a physician is given a report that women have a mean systolic blood
pressure below 140, can she conclude that none of the women have
hypertension (with blood presser greater than 140)? Explain.
12. Identify which of these types of sampling is used: random, systematic, stratified,
cluster or convenience.
a) On the day of the last presidential election, ABC News organized an exit poll
in which specific polling stations were randomly selected and all voters were
surveyed as they left the premises.
b) The author of a statistics textbook once observed sobriety checkpoints in
which every 5th driver was stopped an interviewed.
c) A statistics instructor surveyed all of her students to obtain sample data
consisting of the number of credit cards that college student possess.
9
d) A student organization wants to assess the attitudes of students toward a
proposed change in the hours than the undergraduate library is open. They
randomly select 100 freshmen, 100 sophomores, 100 juniors, and 100 seniors.
13. The following table represents sample data collected on the pulse rates of female
students.
Pulse Rate
Frequency
60 - 89
12
70 – 79
14
80 - 89
11
90 -
99
1
100 – 109
1
110 – 119
0
120 – 129
1
a) Find the class width?
b) Find the class midpoints.
c) Construct a relative frequency table.
d) Construct a cumulative frequency table.
e) Find the mean and the standard deviation.
f) Was the data collected qualitative or quantitative?
g) Was the data collected discrete or continuous?
10
14. Researches collected a simple random sample of the times that 81 college students
required to earn their bachelor’s degrees. The sample has a mean of 4. 8 years
with a standard deviation of 2.2 years. Use a 5% significance level to test the
claim that the mean time for all college students to earn a degree is greater than
4.5 years.
11
15. Listed below are the numbers of years that popes and British monarch (since
1690) lived after their election or coronation. Treat the data as simple random
samples from a larger population.
Popes
9
23
5
21
15
15
3
2
0
6
6
26
10
32
2
18
25
11
11
6
8
25
17
23
19
6
25
13
36
12
15
13
33
59
10
7
63
Monarchs
17
9
a) Are the samples independent or dependent?
b) Find the mean and the standard deviation for the number of years lived after
election of the popes.
c) Find the mean and the standard deviation for the number of years lived after
coronation of the monarchs.
d) Use a 1% significance level to test the claim that the mean longevity for popes
is less than the mean for British monarchs
12
16. Replacement times for CD players are normally distributed with a mean of 8.2
years and a standard deviation of 1.1 years (based on data from “Getting Things
Fixed,” Consumer Reports). If you want to provide a warranty so that only 1% of
the TV sets will be replaced before the warranty expires, what is the time length
of the warranty?
17. True False
The way that a question in a survey is worded rarely has an
effect on the responses.
18. True False
Large samples usually give reasonably accurate results, no
matter how they are drawn.
19. True False
The variance and standard deviation are measures of center.
20. Two variables have a ______________ relationship if the data tend to cluster
around a straight line.
21. True False
If we reject H0, we conclude that H0 is false.
22. True False
If there is no linear relationship between paired date, we
use y as the best predicted value.
24. State the assumptions needed to do a hypothesis test about several population
means (an ANOVA test).
13
25. The following table lists the salaries of randomly selected individuals from four large
metropolitan areas. At the 5% significance level, can you conclude that the mean salary
is different in at least one of the areas?
Pittsburgh
27,800
28,000
25,500
29,150
30,295
Dallas
30,000
33,900
29,750
25,000
34,055
Chicago
32,000
35,800
28,000
38,900
27,245
Minneapolis
30,000
40,000
35,000
33,000
29,805
Anova: Single Factor
SUMMARY
Groups
Pittsburgh
Dallas
Chicago
Minneapolis
Count
5
5
5
5
ANOVA
Source of
Variation
Between Groups
Within Groups
SS
83622620
238558480
Total
322181100
Sum
140745
152705
161945
167805
df
3
16
Average
28149
30541
32389
33561
Variance
3192130
13813030
24975855
17658605
MS
27874206.67
14909905
F
1.869509341
P-value
0.175443187
19
14
F crit
3.238871