1110
1200
740
850
Table 10.7
Exercise 10.9.15
(Solution on p. 467.)
A recent drug survey showed an increase in use of drugs and alcohol among local high school
seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100
national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than
nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60
national seniors reported using them.
Exercise 10.9.16
A student at a four-year college claims that mean enrollment at four–year colleges is higher than
at two–year colleges in the United States. Two surveys are conducted. Of the 35 two–year colleges
surveyed, the mean enrollment was 5068 with a standard deviation of 4777. Of the 35 four-year
colleges surveyed, the mean enrollment was 5466 with a standard deviation of 8191. (Source:
Microsoft Bookshelf )
Exercise 10.9.17
(Solution on p. 467.)
A study was conducted by the U.S. Army to see if applying antiperspirant to soldiers’ feet for a
few days before a major hike would help cut down on the number of blisters soldiers had on their
feet. In the experiment, for three nights before they went on a 13-mile hike, a group of 328 West
Point cadets put an alcohol-based antiperspirant on their feet. A “control group” of 339 soldiers
put on a similar, but inactive, preparation on their feet. On the day of the hike, the temperature
reached 83 ◦ F. At the end of the hike, 21% of the soldiers who had used the antiperspirant and 48%
of the control group had developed foot blisters. Conduct a hypothesis test to see if the proportion
of soldiers using the antiperspirant was significantly lower than the control group. (Source: U.S.
Army study reported in Journal of the American Academy of Dermatologists)
Exercise 10.9.18
We are interested in whether the proportions of female suicide victims for ages 15 to 24 are the
same for the white and the black races in the United States. We randomly pick one year, 1992,
to compare the races. The number of suicides estimated in the United States in 1992 for white
females is 4930. 580 were aged 15 to 24. The estimate for black females is 330. 40 were aged 15 to
24. We will let female suicide victims be our population. (Source: the National Center for Health
Statistics, U.S. Dept. of Health and Human Services)
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PROPORTIONS
Exercise 10.9.19
(Solution on p. 468.)
At Rachel’s 11th birthday party, 8 girls were timed to see how long (in seconds) they could hold
their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping.
The girls thought that the mean difference between their jumping and relaxed times would be 0.
Test their hypothesis.
Relaxed time (seconds)
Jumping time (seconds)
26
21
47
40
30
28
22
21
23
25
45
43
37
35
29
32
Table 10.8
Exercise 10.9.20
Elizabeth Mjelde, an art history professor, was interested in whether the value from the Golden
Ratio formula,
larger+smaller dimension was the same in the Whitney Exhibit for works from 1900
larger dimension
– 1919 as for works from 1920 – 1942. 37 early works were sampled. They averaged 1.74 with
a standard deviation of 0.11. 65 of the later works were sampled. They averaged 1.746 with a
standard deviation of 0.1064. Do you think that there is a significant difference in the Golden
Ratio calculation? (Source: data from Whitney Exhibit on loan to San Jose Museum of Art )
Exercise 10.9.21
(Solution on p. 468.)
One of the questions in a study of marital satisfaction of dual–career couples was to rate the state-
ment, “I’m pleased with the way we divide the responsibilities for childcare.” The ratings went
from 1 (strongly agree) to 5 (strongly disagree). Below are ten of the paired responses for hus-
bands and wives. Conduct a hypothesis test to see if the mean difference in the husband’s versus
the wife’s satisfaction level is negative (meaning that, within the partnership, the husband is hap-
pier than the wife).
Wife’s score
2
2
3
3
4
2
1
1
2
4
Husband’s score
2
2
1
3
2
1
1
1
2
4
Table 10.9
Exercise 10.9.22
Ten individuals went on a low–fat diet for 12 weeks to lower their cholesterol. Evaluate the data
below. Do you think that their cholesterol levels were significantly lowered?
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Starting cholesterol level
Ending cholesterol level
140
140
220
230
110
120
240
220
200
190
180
150
190
200
360
300
280
300
260
240
Table 10.10
Exercise 10.9.23
(Solution on p. 468.)
Mean entry level salaries for college graduates with mechanical engineering degrees and elec-
trical engineering degrees are believed to be approximately the same.
(Source:
http://
www.graduatingengineer.com10 ). A recruiting office thinks that the mean mechanical engineer-
ing salary is actually lower than the mean electrical engineering salary. The recruiting office ran-
domly surveys 50 entry level mechanical engineers and 60 entry level electrical engineers. Their
mean salaries were $46,100 and $46,700, respectively. Their standard deviations were $3450 and
$4210, respectively. Conduct a hypothesis test to determine if you agree that the mean entry level
mechanical engineering salary is lower than the mean entry level electrical engineering salary.
Exercise 10.9.24
A recent year was randomly picked from 1985 to the present. In that year, there were 2051 Hispanic
students at Cabrillo College out of a total of 12,328 students. At Lake Tahoe College, there were
321 Hispanic students out of a total of 2441 students. In general, do you think that the percent
of Hispanic students at the two colleges is basically the same or different? (Source: Chancellor’s
Office, California Community Colleges, November 1994 )
Exercise 10.9.25
(Solution on p. 468.)
Eight runners were convinced that the mean difference in their individual times for running one
mile versus race walking one mile was at most 2 minutes. Below are their times. Do you agree
that the mean difference is at most 2 minutes?
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PROPORTIONS
Running time (minutes)
Race walking time (minutes)
5.1
7.3
5.6
9.2
6.2
10.4
4.8
6.9
7.1
8.9
4.2
9.5
6.1
9.4
4.4
7.9
Table 10.11
Exercise 10.9.26
Marketing companies have collected data implying that teenage girls use more ring tones on their
cellular phones than teenage boys do. In one particular study of 40 randomly chosen teenage girls
and boys (20 of each) with cellular phones, the mean number of ring tones for the girls was 3.2
with a standard deviation of 1.5. The mean for the boys was 1.7 with a standard deviation of 0.8.
Conduct a hypothesis test to determine if the means are approximately the same or if the girls’
mean is higher than the boys’ mean.
Exercise 10.9.27
(Solution on p. 468.)
While her husband spent 2½ hours picking out new speakers, a statistician decided to determine
whether the percent of men who enjoy shopping for electronic equipment is higher than the per-
cent of women who enjoy shopping for electronic equipment. The population was Saturday af-
ternoon shoppers. Out of 67 men, 24 said they enjoyed the activity. 8 of the 24 women surveyed
claimed to enjoy the activity. Interpret the results of the survey.
Exercise 10.9.28
We are interested in whether children’s educational computer software costs less, on average,
than children’s entertainment software. 36 educational software titles were randomly picked from
a catalog. The mean cost was $31.14 with a standard deviation of $4.69. 35 entertainment software
titles were randomly picked from the same catalog. The mean cost was $33.86 with a standard
deviation of $10.87. Decide whether children’s educational software costs less, on average, than
children’s entertainment software. (Source: Educational Resources, December catalog)
Exercise 10.9.29
(Solution on p. 468.)
Parents of teenage boys often complain that auto insurance costs more, on average, for teenage
boys than for teenage girls. A group of concerned parents examines a random sample of insurance
bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From
past years, it is known that the population standard deviation for each group is $180. Determine
whether or not you believe that the mean cost for auto insurance for teenage boys is greater than
that for teenage girls.
Exercise 10.9.30
A group of transfer bound students wondered if they will spend the same mean amount on texts
and supplies each year at their four-year university as they have at their community college. They
conducted a random survey of 54 students at their community college and 66 students at their
local four-year university. The sample means were $947 and $1011, respectively. The population
standard deviations are known to be $254 and $87, respectively. Conduct a hypothesis test to
determine if the means are statistically the same.
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Exercise 10.9.31
(Solution on p. 468.)
Joan Nguyen recently claimed that the proportion of college–age males with at least one pierced
ear is as high as the proportion of college–age females. She conducted a survey in her classes. Out
of 107 males, 20 had at least one pierced ear. Out of 92 females, 47 had at least one pierced ear. Do
you believe that the proportion of males has reached the proportion of females?
Exercise 10.9.32
Some manufacturers claim that non-hybrid sedan cars have a lower mean miles per gallon (mpg)
than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 31 mpg with a
standard deviation of 7 mpg. Thirty-one non-hybrid sedans get a mean of 22 mpg with a standard
deviation of 4 mpg. Suppose that the population standard deviations are known to be 6 and 3,
respectively. Conduct a hypothesis test to the manufacturers claim.
Questions Exercise 10.9.33 – Exercise 10.9.37 refer to the Terri Vogel’s data set (see Table of Contents).
Exercise 10.9.33
(Solution on p. 468.)
Using the data from Lap 1 only, conduct a hypothesis test to determine if the mean time for com-
pleting a lap in races is the same as it is in practices.
Exercise 10.9.34
Repeat the test in Exercise 10.9.33, but use Lap 5 data this time.
Exercise 10.9.35
(Solution on p. 469.)
Repeat the test in Exercise 10.9.33, but this time combine the data from Laps 1 and 5.
Exercise 10.9.36
In 2 – 3 complete sentences, explain in detail how you might use Terri Vogel’s data to answer the
following question. “Does Terri Vogel drive faster in races than she does in practices?”
Exercise 10.9.37
(Solution on p. 469.)
Is the proportion of race laps Terri completes slower than 130 seconds less than the proportion of
practice laps she completes slower than 135 seconds?
Exercise 10.9.38
"To Breakfast or Not to Breakfast?" by Richard Ayore
In the American society, birthdays are one of those days that everyone looks forward to. People of
different ages and peer groups gather to mark the 18th, 20th, . . . birthdays. During this time, one
looks back to see what he or she had achieved for the past year, and also focuses ahead for more
to come.
If, by any chance, I am invited to one of these parties, my experience is always different. Instead
of dancing around with my friends while the music is booming, I get carried away by memories
of my family back home in Kenya. I remember the good times I had with my brothers and sister
while we did our daily routine.
Every morning, I remember we went to the shamba (garden) to weed our crops. I remember one
day arguing with my brother as to why he always remained behind just to join us an hour later. In
his defense, he said that he preferred waiting for breakfast before he came to weed. He said, “This
is why I always work more hours than you guys!”
And so, to prove his wrong or right, we decided to give it a try. One day we went to work as usual
without breakfast, and recorded the time we could work before getting tired and stopping. On
the next day, we all ate breakfast before going to work. We recorded how long we worked again
before getting tired and stopping. Of interest was our mean increase in work time. Though not
sure, my brother insisted that it is more than two hours. Using the data below, solve our problem.
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PROPORTIONS
Work hours with breakfast
Work hours without breakfast
8
6
7
5
9
5
5
4
9
7
8
7
10
7
7
5
6
6
9
5
Table 10.12
10.9.2 Try these multiple choice questions.
For questions Exercise 10.9.39 – Exercise 10.9.40, use the following information.
A new AIDS prevention drugs was tried on a group of 224 HIV positive patients. Forty-five (45) patients
developed AIDS after four years. In a control group of 224 HIV positive patients, 68 developed AIDS after
four years. We want to test whether the method of treatment reduces the proportion of patients that develop
AIDS after four years or if the proportions of the treated group and the untreated group stay the same.
Let the subscript t= treated patient and ut= untreated patient.
Exercise 10.9.39
(Solution on p. 469.)
The appropriate hypotheses are:
A. Ho : pt < put and Ha : pt ≥ put
B. Ho : pt ≤ put and Ha : pt > put
C. Ho : pt = put and Ha : pt = put
D. Ho : pt = put and Ha : pt < put
Exercise 10.9.40
(Solution on p. 469.)
If the p -value is 0.0062 what is the conclusion (use α = 0.05 )?
A. The method has no effect.
B. There is sufficient evidence to conclude that the method reduces the proportion of HIV positive
patients that develop AIDS after four years.
C. There is sufficient evidence to conclude that the method increases the proportion of HIV posi-
tive patients that develop AIDS after four years.
D. There is insufficient evidence to conclude that the method reduces the proportion of HIV pos-
itive patients that develop AIDS after four years.
Exercise 10.9.41
(Solution on p. 469.)
Lesley E. Tan investigated the relationship between left-handedness and right-handedness and
motor competence in preschool children. Random samples of 41 left-handers and 41 right-handers
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455
were given several tests of motor skills to determine if there is evidence of a difference between the
children based on this experiment. The experiment produced the means and standard deviations
shown below. Determine the appropriate test and best distribution to use for that test.
Left-handed
Right-handed
Sample size
41
41
Sample mean
97.5
98.1
Sample standard deviation
17.5
19.2
Table 10.13
A. Two independent means, normal distribution
B. Two independent means, student’s-t distribution
C. Matched or paired samples, student’s-t distribution
D. Two population proportions, normal distribution
For questions Exercise 10.9.42 – Exercise 10.9.43, use the following information.
An experiment is conducted to show that blood pressure can be consciously reduced in people trained in a
“biofeedback exercise program.” Six (6) subjects were randomly selected and the blood pressure measure-
ments were recorded before and after the training. The difference between blood pressures was calculated
(after − before) producing the following results: xd = −10.2 sd = 8.4. Using the data, test the hypothesis
that the blood pressure has decreased after the training,
Exercise 10.9.42
(Solution on p. 469.)
The distribution for the test is
A. t5
B. t6
C. N (−10.2, 8.4)
D. N −10.2, 8.4
√6
Exercise 10.9.43
(Solution on p. 469.)
If α = 0.05, the p-value and the conclusion are
A. 0.0014; There is sufficient evidence to conclude that the blood pressure decreased after the
training
B. 0.0014; There is sufficient evidence to conclude that the blood pressure increased after the train-
ing
C. 0.0155; There is sufficient evidence to conclude that the blood pressure decreased after the
training
D. 0.0155; There is sufficient evidence to conclude that the blood pressure increased after the
training
For questions Exercise 10.9.44– Exercise 10.9.45, use the following information.
The Eastern and Western Major League Soccer conferences have a new Reserve Division that allows new
players to develop their skills. Data for a randomly picked date showed the following annual goals.
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PROPORTIONS
Western
Eastern
Los Angeles 9
D.C. United 9
FC Dallas 3
Chicago 8
Chivas USA 4
Columbus 7
Real Salt Lake 3
New England 6
Colorado 4
MetroStars 5
San Jose 4
Kansas City 3
Table 10.14
Conduct a hypothesis test to determine if the Western Reserve Division teams score, on average, fewer goals
than the Eastern Reserve Division teams. Subscripts: 1 Western Reserve Division (W); 2 Eastern Reserve
Division (E)
Exercise 10.9.44
(Solution on p. 469.)
The exact distribution for the hypothesis test is:
A. The normal distribution.
B. The student’s-t distribution.
C. The uniform distribution.
D. The exponential distribution.
Exercise 10.9.45
(Solution on p. 469.)
If the level of significance is 0.05, the conclusion is:
A. There is sufficient evidence to conclude that the W Division teams score, on average, fewer
goals than the E teams.
B. There is insufficient evidence to conclude that the W Division teams score, on average, more
goals than the E teams.
C. There is insufficient evidence to conclude that the W teams score, on average, fewer goals than
the E teams score.
D. Unable to determine.
Questions Exercise 10.9.46 – Exercise 10.9.48 refer to the following.
Neuroinvasive West Nile virus refers to a severe disease that affects a person’s nervous system . It
is spread by the Culex species of mosquito.
In the United States in 2010 there were 629 reported
cases of neuroinvasive West Nile virus out of a total of 1021 reported cases and there were 486 neu-
roinvasive reported cases out of a total of 712 cases reported in 2011.
Is the 2011 proportion of
neuroinvasive West Nile virus cases more than the 2010 proportion of neuroinvasive West Nile virus
cases?
Using a 1% level of significance, conduct an appropriate hypothesis test.
(Source: http://
http://www.cdc.gov/ncidod/dvbid/westnile/index.htm 11 )
• “2011” subscript: 2011 group.
• “2010” subscript: 2010 group
Exercise 10.9.46
(Solution on p. 469.)
This is:
A. a test of two proportions
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B. a test of two independent means
C. a test of a single mean
D. a test of matched pairs.
Exercise 10.9.47
(Solution on p. 469.)
An appropriate null hypothesis is:
A. p2011 ≤ p2010
B. p2011 ≥ p2010
C. µ 2011 ≤ µ 2010
D. p2011 > p2010
Exercise 10.9.48
(Solution on p. 469.)