Transcript N_testgameSOLUTIONS_APS

A random sample of 44 individuals with a B.S. degree
in accounting who had started with a “Big Eight”
accounting firm and subsequently changed jobs
resulted in a mean time to change of 35.02 months
and a standard deviation of 18.94 months. At the 0.05
level of significance, is there sufficient evidence to
support the claim that true mean time to change
exceeds 24 months.
1 SAMPLE T-TEST
A study of zinc-deficient mothers was conducted to
determine whether zinc supplementation during pregnancy
results in babies with increased weights at birth. Sample data
are listed below. The weights were measured in grams.
Using a 0.05 significance level, is there sufficient evidence to
support the claim that zinc supplementation does result in
increased birth weights?
n
Mean
Standard
Deviation
Zinc
Supplement
294
3214
Placebo
669
728
286
3088
2 SAMPLE T-TEST
A study of sport and compact car colors shows that 15.2% are
green, 14.4% are white, 19.8% are red, 11.2% are black and
39.4% are other colors (based on data from DuPont
Automotive as reported in USA Today). When 100 trucks and
vans are randomly selected, it is found that 16 are green, 24
are white, 16 are red, none are black, and 44 are other colors.
Is there sufficient evidence to support the claim that the color
distribution for trucks and vans is different from the color
distribution for sport and compact cars? Use a 0.05 level of
significance.
CHI-SQUARED G.O.F.
A student organization uses the proceeds from a particular
soft drink dispensing machine to finance its activities. The
price per can had been $.50 for a long time, and the average
daily revenue during that period $50.00. The price was
recently increased to $.60 per can. A random sample of n =
20 days subsequent to the price increase yielded a sample
average revenue and sample standard deviation of $47.30
and $4.20, respectively. Does this data suggest that the true
average daily revenue has decreased from its value prior to
the price increase? Use a .05 level of significance.
1 SAMPLE T-TEST
Clinical test of allergy drug Seldane yielded results
summarized in the accompanying table. At the 0.05
significance level, test the claim that the occurrence of
headaches is independent of the group (Seldane,
Placebo, control). Based on these results, should Seldane
users be concerned about getting headaches?
Headache
No Headache
Seldane
49
743
Placebo
49
616
Control
24
602
CHI-SQUARED INDEPENDENCE
Twelve Dozenol tablets are tested for solubility before and
after being stored for one year. The indexes of solubility are
given in the table below
Before 472 487 506 512 489 403 511 495 504 494 462
After
562 512 523 528 554 513 530 524 510 524 508
Test the claim that the solubility is greater after being stored for
one year.
MATCHED PAIR T-TEST
A test question is considered good if it discriminates between
unprepared and prepared students. The first question on a
test was answered correctly by 23 of 50 unprepared students
and by 45 of 80 prepared students. At the 0.05 significance
level, test the claim that the proportion of unprepared
students who answer the question correctly is less than the
proportion of prepared students who answer it correctly.
2 SAMPLE PROPORTION Z-TEST
The article “Caffeine Knowledge, Attitudes and Consumption
in Adult Women” reported the following summary data on
daily caffeine consumption of a random sample of adult
women:
n = 47
x = 215 mg
s = 235 mg
Suppose that it had previously been believed that the mean
consumption of caffeine was at most 200 mg. Does the
given data contradict this prior belief? Use a 0.01 level of
significance.
1 SAMPLE T-TEST
Academic dishonesty continues to be a problem on
college and university campuses. One form of
dishonesty is to look at notes during an exam or quiz.
One study reported that in a random sample of 480
students, 124 said they had looked at notes during an
exam or quiz. At the 0.05 level of significance is there
sufficient evidence to conclude that more than 20% of
all students engage in this particular form of academic
dishonesty.
1 SAMPLE PROPORTION Z-TEST
A sociologist conducts a study to determine if there is a
relationship between cheating on exams and socioeconomic
status. A random sample of 750 high school students yields
the following results:
Cheat
Don’t Cheat
High Status
118
282
Low Status
82
268
What is the conclusion about cheating and
socioeconomic status at the 5% significance level?
CHI-SQUARED INDEPENDENCE
A pharmaceutical firm would like to show that taking a
particular mixture of vitamins and natural herbs would raise
the IQ of a teenager. A sample of 15 teenagers is chosen,
and their IQs are measured before and after taking the
vitamin-herb mixture for 1 year. The individual results are as
follows:
Before 103 98
After
95 107 112 125 111 89 100 121 114 107 95 106 115
107 100 96 104 110 129 110 87 89
121 117 105 98 108 119
The pharmaceutical firm claims that after taking the vitaminherb mixture, teenagers have a higher than average IQ.
(Average IQ is 100) Do the data support their conclusion?
1 SAMPLE T-TEST
A sporting goods manufacturer who produces both white
and yellow golf balls claims that more than 75% of all golf
balls sold are white. A marketing study of the purchases of
white and yellow golf balls at a number of stores showed
that of 470 balls sold, 410 were white and 60 were yellow. Is
there sufficient evidence to support the researcher’s claim?
1 SAMPLE PROPORTION Z-TEST
Do you have an insatiable craving for chocolate or some
other food? Since many North Americans apparently do,
psychologists are designing scientific studies to examine
the phenomenon. A survey of 1,000 McMaster University
students revealed that 97% of women in the study
acknowledged specific food cravings while only 67% of
the men did. Assume that 600 of the respondents were
women and 400 were men. Is there sufficient evidence to
claim the true proportion of women who acknowledge
having food cravings exceeds the corresponding
proportion of men?
2 SAMPLE PROPORTION Z-TEST
The pain reliever currently used in a hospital is known to
bring relief to patients in a mean time of 3.5 minutes. To
compare a new pain reliever with the current one, the new
drug is administered to a random sample of 50 patients.
The mean time to relief for the sample of patients is 2.89
minutes and the standard deviation is 1.14 minutes. Do
the data provide sufficient evidence to conclude that the
new drug was effective in reducing the mean time until a
patient receives relief from pain?
1 SAMPLE T-TEST
A homophone is a word whose pronunciation is the same as
that of another word having a different meaning and spelling.
Twenty Alzheimer’s patients were asked to spell 24
homophone pairs given in random order, then the number of
homophone confusions (e.g., spelling doe given the context,
bake bread dough) was recorded for each patient. One year
later the same test was given to the same patients. Perform
an analysis to test if Alzheimer’s patients show a significant
increase in mean homophone confusion errors over time.
P#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
T1
5
1
0
1
0
2
5
1
0
5
7
0
3
5
7
10
5
6
9
11
T2
5
3
0
1
1
1
6
2
9
8
10
3
9
8
12
16
5
3
6
8
MATCHED PAIR T-TEST
A verbal test was given to a group of children, ranging from
10-12 years of age, in order to study the relationship between
the number of words used and the silence interval before
response. Each subject was asked a series of questions and
the total number of words used in answering was recorded.
The time (in seconds) before the subject responded to each
question was also recorded. Is there evidence that there is a
relationship between number of words and silence time?
Subject #
1
2
3
4
5
6
7
8
Total Words
61 70 42 52 91 63 71 55
Silence Time
23 37 38 25 17 21 42 16
LINEAR REGRESSION T-TEST
Failure to meet payments on student loans guaranteed by
the US government has been a major problem both for
banks and for the government. Approximately 50% of all
student loans guaranteed by the government are in default.
A random sample of 350 loans to college students in one
region of the United States indicates that 147 loans are in
default. Do the data indicate that the proportion of student
loans in default in this area of the country differs from the
proportion of all student loans in the US?
1 SAMPLE PROPORTION Z-TEST
The American Journal of Public health (July 1995) reported on a
population based study of trauma in Hispanic children. One of the
objectives of the study was to compare the use of protective devices
in motor vehicles used to transport Hispanic and non-Hispanic white
children. On the basis of data collected from the San Diego Regional
Trauma System, 792 children treated for injuries sustained in vehicular
accidents were classified according to ethnic status (Hispanic or nonHispanic white) and seatbelt usage (worn or not worn) during the
accident.
Hispanic Non-Hispanic White
Seatbelt Worn
31
Seatbelt Not Worn 283
283
330
Conduct a test to determine whether seatbelt usage in motor vehicle
accidents depends on ethnic status in the San Diego Regional
Trauma System.
CHI-SQUARED INDEPENDENCE
The changing ecology of the Everglades National Park in
Florida, considered a national treasure by many, has been the
subject of much environmental research. One water quality
parameter of concern in the park is the total phosphorus level.
Suppose that the EPA makes 12 measurements in one
section of the park, yielding a mean level of total phosphorus
at 12.3 parts per billion (ppb) and a standard deviation of 5.4
ppb. The EPA wants to test whether the data support the
conclusion that the mean level is less than 15 ppb.
1 SAMPLE T-TEST
Is the maximum oxygen uptake, a measure often used by
psychologist to indicate an individual’s state of cardiovascular
fitness, related to the performance of distance runners? Six
long-distance runners submitted to treadmill tests for
determination of their maximum oxygen uptake. The results,
along with each runner’s best mile time (in seconds), are shown
in the table.
Athlete Maximum Oxygen
Uptake
Mile
Time
1
63.3
241.5
2
60.1
249.8
3
53.6
246.1
4
58.8
232.4
5
67.5
237.2
6
62.5
238.4
LINEAR REGRESSION T-TEST