2. One criticism of reading comprehension tests is that while they may measure reading
comprehension, they also measure other factors not related to reading comprehension. A reading
comprehension (RC) test on a major college entrance exam provides short English prose
passages, and the examinees answer a set of multiple-choice items about the passage. To see if
particular items measure something other than RC, investigators gave the RC test without the
reading passages to a random sample of psychology students. The investigators reasoned that if
questions were measuring knowledge or memory rather than just RC, students would answer
questions at a higher rate than chance (20%, since there were 5 choices for each question.)
Suppose that on one question, 30 out of 100 examinees answered the question correctly. Is this
sufficient evidence that students are using more than just reading comprehension to answer this
question? Test the relevant hypothesis using a = .05 .
2. A manufacturer of gunpowder has developed a new powder that is designed to produce a
muzzle velocity equal to 3000 feet per second. Eight shells are loaded with the charge and
muzzle velocities measured. The resulting velocities are as follows:
3005 2925 2935 2965 2995 3005 2935 2905
Do the data present sufficient evidence to indicate that the average velocity differs from 3000
feet per second? Conduct test of hypothesis at =.05.
1. A machine is set to produce bolts with a mean length of 1 inch. Bolts that are too long or too short do
not meet the customer’s specifications and must be rejected. To avoid producing too many rejects, the
bolts produced by the machine are sampled from time to time and tested as a check to see whether the
machine is still operating properly. Suppose fifty bolts have been sampled, and x =1.02 and s=.04. Do the
data provide sufficient evidence to conclude that the machine is producing bolts with a mean length not
equal to 1 inch? Use =.01.
2. In a test of the effectiveness of a device that is supposed to increase gasoline mileage in
automobiles, 12 cars were run over a prescribed course both with and without the device. The
mileages are given below. Is there evidence that the device is effective. Conduct hypothesis test
at =.05.
Car
1
2
3
4
5
6
7
8
Without Device
21
30
29.8
27.3
27.7
33.1
18.8
26.2
With Device
20.6
29.9
30.7
26.5
26.7
32.8
21.7
28.2
9
10
11
12
28
18.9
29.3
21
28.9
19.9
32.4
22
3. Rapid drainage of floodwater is crucial to prevent damage during heavy rains. Several designs
for a drainage canal were considered for a certain city. Each design was tested four times, to
determine how long it took to drain the water in a reservoir. The following table presents the
drainage times, in minutes.
Type 1
41.4
43.4
50.0
41.2
Type 2
38.7
48.3
51.1
38.3
Type 3
32.6
33.7
34.8
22.5
Type 4
26.3
30.9
33.3
23.8
Type 5
44.9
47.2
48.5
37.1
4. Ionizing radiation is being given increasing attention as a method for preserving horticultural products.
A study reports that 153 of 180 irradiated garlic bulbs were marketable (no external sprouting, rotting, or
softening) 240 days after treatment, whereas only 117 of 180 untreated bulbs were marketable after this
length of time. Does this data suggest that ionizing radiation is beneficial as far as marketability is
concerned? Use =.05.
4) The University of Idaho uses thousands of fluorescent light bulbs each year. The brand of bulb
it currently uses has a mean life of 900 hours. A manufacturer claims that its new brand of bulbs,
which cost the same as the brand the university currently uses, has a mean life of more than 900
hours. The university has decided to purchase the new brand if, when tested, the test evidence
supports the manufacturer’s claim at =.01. Suppose sixty-four bulbs were tested with the
following results:
s= 80 hours
x = 930 hours
Will the University of Idaho purchase the new brand of fluorescent bulbs? Conduct test of
hypothesis at =.05.
Example An assertiveness training course has just been added to the services offered by a counseling center. To
measure its effectiveness, ten students are given a test at the beginning of the course and again at the end. A high
score on the test implies high assertiveness. Do the data provide sufficient evidence to conclude that people are more
assertive after taking the course? =.05
Before Course
50
62
51
41
63
56
49
67
42
57
After Course
65
68
52
43
60
70
48
69
53
61
Example Opinion polls often provide information on how different groups’ opinions vary on controversial issues. A
random sample of 102 registered voters was taken from the Supervisor of Election’s roll. Each of the registered
voters was asked the following two questions:
1. What is your political party affiliation?
2. Are you in favor of increased arms spending?
The results are summarized in the table below.
Opinion
Favor
No favor
Democrat
16
24
Party
Republican
21
17
None
11
13
Example Three different brands of automobile batteries, each one having 42-month warranty, were
included in a study of battery lifetime. A random sample of batteries of each brand was selected and
lifetime (in months) was determined, resulting in the following data.
Brand 1: 45
Brand 2: 39
Brand 3: 50
38
44
46
52
50
43
47
54
48
45
48
57
42
46
44
43
40
48
2. Two antibiotics are to be compared. Cultures from 387 out 450 patients treated with antibiotic A showed
antibacterial activity while cultures from 278 out of 350 patients treated with antibiotic B showed similar activity. Is
there sufficient evidence to conclude a difference in the proportion of active cultures for the two antibiotics? Use
=.05.
3. The paper “Undergraduate Marijuana Use and Anger” (J. Of Psychol. (1988):343-347) reported that
the mean and standard deviation on an anger expression scale were x =42.72 and s=6.05, respectively,
for a sample of n=47 frequent marijuana users. Suppose that the population mean score for nonusers is
41.5. Do the data indicate that frequent users have a mean anger expression score that is higher than for
nonusers? Use=.05. Report p-value.
Example Are the educational aspirations of students related to family income? This question was investigated in the
article “Aspirations and Expectations of High School Youth” (Int. J. of Comp. Soc. (1975): 25). The accompanying
4 X 3 table resulted from classifying 273 students according to expected level of education and family income. Does
the data indicate that education aspirations and family income are not independent? Conduct test using = .05.
____________________________________________________________________
Income
Aspired Level
Low
Middle
High
Some High School
9
11
9
High School Graduate
44
52
41
Some College
13
23
12
College Graduate
10
22
27
6. Twenty volunteers at a cold research institute caught a cold after after having been exposed to various cold
viruses. Ten of the volunteers were randomly selected to receive tablets containing 1 gram of vitamin C. These
tablets were taken four times a day. The control group, consisting of the other 10 volunteers, was given placebo
tablets that looked and tasted exactly like the vitamin C ones. This was continued for each volunteer until a doctor,
who did not know whether one volunteer was receiving vitamin C or the placebo, decided that the volunteer was no
longer suffering from the cold. The length of time the cold lasted was then recorded. At the end of the experiment,
the following data resulted:
Treated With Vitamin C
5.5
6.0
7.0
6.0
7.5
7.5
5.5
7.0
6.5
6.0
Treated With Placebo
6.5
6.0
8.5
7.0
6.5
7.5
6.5
7.5
6.0
8.0
Is there sufficient evidence to conclude that the mean time for patients treated with vitamin C is less than the mean
time for the patients treated with placebo? Use =.05.
Questions 9 to 13: A gambler wanted to test whether or not a die was fair. He rolled the die 180 times and got the
results shown below. For example, the number “1” appeared on 40 rolls.
Die Result
Frequency
1
40
2
40
3
30
4
30
5
20
6
20
Total
180
3. An experiment was conducted to compare the mean number of tapeworms in the stomachs of sheep
that had been treated for worms against the mean number in those that were untreated. A sample of 14
worm-infected lambs was randomly divided into two groups. Seven were injected with the drug and the
remainder were left untreated. After a six-month period, the lambs were slaughtered and the following
worm counts were recorded:
Drug-treated sheep
Untreated Sheep
18
40
43
54
28
26
50
63
16
21
32
37
13
39
Test a hypothesis that there is no difference in the mean number of worms between treated and untreated
lambs. Assume that the drug cannot increase the number of worms and hence use the alternative
hypothesis that the mean for treated lambs is less than the mean for untreated lambs. Use =.05.
6. In previous presidential elections in a given locality, 50% of the registered voters were Republicans, 40% were
Democrats, and 10% were registered as independents. Prior to the upcoming election, a random sample of 200
registered voters showed that 90 were registered as Republicans, 80 as Democrats, and 30 as independents. Is there
sufficient evidence to conclude that the distribution of registered voters in the population is different from that in
previous election years. Conduct hypothesis test using =.01.
8. Replacement of paint on highways and streets represents a large investment of funds by state and local
governments each year. A new, cheaper brand of paint is tested for durability after one month’s time by
reflectometer readings. For the new brand to be acceptable, it must have a mean reflectometer reading greater than
19.6. The sample data, based on 35 randomly selected readings, show x =19.8 and s=1.5. Is there sufficient
evidence to conclude that the new brand is acceptable? Conduct hypothesis test using =.05.
5. A staff member of an emergency medical service wishes to determine whether the number of accidents is equally
distributed during the week. A week was selected at random, and the following data were obtained. Test the
hypothesis that the number of accidents is equally distributed throughout the week, at =.05.
Day
# of accidents
Monday
28
Tuesday
32
Wednesday
15
Thursday
14
Friday
38
Saturday
43
Sunday
19
EXAMPLE The paper "Orchard Floor Management Utilizing
Soil-Applied Coal Dust for Frost Protection" reported the
following values for soil heat flux of eight plots covered with
coal dust.
34.7 35.4 34.7 37.7 32.5 28.0 18.4 24.9
Conduct the following test of hypothesis Ho: = 29 (the
mean soil heat flux for plots covered only with grass) vs
Ha:  > 29? Carry out a hypothesis test at =.05.
Example A study was conducted to help determine who takes advantage of sales and specials at food stores that
advertise in newspapers. Shoppers were asked whether they usually check the advertisements before shopping and
which of the following income brackets they fit into: annual income below $5,000, between $5,000 and $15,000,
between $15,000 and $25,000, between $25,000 and $35,000, or over $35,000. The data are given below. Test to see
if income level affects whether a shopper checks food store advertisements. Use =.05.
Yes
No
Less than 5
33
3
5 to < 15
62
8
15 to < 25
31
19
25 to < 35
14
15
35 and over
6
14
An experiment is conducted to compare the starting
salaries of male and female college graduates who
find jobs. Pairs are formed by choosing a male and a
female with the same-major and similar grade point
averages. Suppose a random sample of ten pairs is
formed in this manner and the starting salary of each
person is conducted.
Pair
1
2
3
4
5
6
7
8
Male
$14,300
16,500
15,400
13,500
18,500
12,800
14,500
16,200
Female
$13,800
16,600
14,800
13,500
17,600
13,000
14,200
15,100
9
10
13,400
14,200
13,200
13,500
1. In a sample of 88 adults selected randomly from one town, it is found that 6 of them have been exposed
to a particular strain of the flu. At the 0.01 significance level, test the claim that the proportion of all
adults in the town that have been exposed to this strain of the flue differs from the nationwide proportion
of .08.
Example A development engineer is interested in determining if varying the cotton content in a
synthetic fiber affects the tensile strength.
% Cotton
15
7
20
12
25
14
30
19
35
7
Observed Tensile Strength
7
15
11
17
12
18
18
18
19
25
22
19
10
11
15
9
18
19
23
11
Example A law student believes that the proportion of registered Republican in favor of additional tax incentives is
greater than the proportion of registered democrats in favor of such incentives. The student acquired independent
random samples of 200 republicans and 200 Democrats and found that 109 Republicans and 86 Democrats in favor
of additional tax incentives.
Example The accompanying two-way table was constructed using data in the paper “Television Viewing and
Physical Fitness in Adults” (Research Quarterly for Exercise and Sport (1990): 315-320). The author hoped to
determine whether time spent watching television is related to cardiovascular fitness. Subjects were asked about
their television-viewing time (per day, rounded to the nearest hour) and were classified as physically fit if they
scored in the excellent or very good category on a step test. (10 pts.)
0
1-2
3-4
5 or more
Physically Fit
35
101
28
4
Not Physically Fit
147
629
222
34
Example State DMV records indicate that of all vehicles undergoing emissions testing during the previous year,
70% passed on the first try. A random sample of 200 cars tested in a particular county during the current year yields
160 that passed on the initial test. Does this suggest that the population proportion for this county during the current
year differs from the previous statewide proportion? Conduct hypothesis test using   .05.
Example Criminologists have long debated whether there is a relationship between weather and violent crime. The
author of the paper “Is there a Season for Homicide?” (Criminology (1988): 287-296) classified 1361 homicides
according to season, resulting in the accompanying data. Does this data support the theory that the homicide rate is
not the same over the four seasons? Test the relevant hypotheses using =.05.
_____________________________________________________
Season
Winter
Spring
Summer
Fall
328
334
372
327
EXAMPLE Some investigators think that the concentration (mg/ml) of a particular antigen in
supernatant fluids could be related to the onset of meningitis in infants. The accompanying data
is typical of that given in plots appearing in the paper “Type-Specific Capsular Antigen is
Associated with virulence in Late-Onset Group B Streptococcal Type III Disease” (Infection and
Immunity(1984):124-129)
Asymptomatic infants
Infants with late onset sephis
Infants with late onset meningitis
1.56
1.51
1.21
1.06
1.78
1.34
.87
1.45
1.95
1.39
1.13
2.00
.71
1.87
2.27
.87
1.89
.88
.95
1.07
1.67
1.51
1.72
2.57
Example An experimenter wished to determine whether there is a relationship between hair color and eye color.
One hundred people were randomly selected and the eyes and hair of each person were judged to be light or dark. A
summary of the number of people in each of the four categories is shown in the table. Do the data provide sufficient
evidence to indicate a relationship between eye and hair color? Test using =.05.
Light Eyes
Dark Eyes
Light Hair
31
14
Dark Hair
21
34
Example The Los Angeles Times (Oct. 17, 1984) reported the color distribution for plain M&M’s was: 40% brown,
20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s
was classified according to color, resulting in the given data. Using =.05, determine if the data suggests that the
published color distribution is incorrect.
Frequency
Brown
45
Yellow
13
Orange
17
Green
7
Tan
18
Example In a recent survey of county high school students (n1=100 males and n2=100 females), 58 of the males and
46 of the females sampled said they consume alcohol on a regular basis.
Example Bowker and Lieberman (1972) gave the results for tests of two thermostats used in irons that
were made by an old supplier and a new supplier. Twenty three thermostats from each supplier were
tested at a setting of 550 F. The actual temperature, measured with a thermocouple, are given below. Do
the data provide evidence of differences in the mean temperatures for the thermostats from the two
suppliers? Conduct test at =.05.
new
530.3
549.4
551.7
old
559.7
554.8
544.6
549.9
536.7
538.8
559.1
538.6
565.4
550.0
554.7
569.1
559.3
544.0
566.3
556.9
558.8
543.3
555.0
551.1
554.9
554.9
536.1
550.7
551.1
538.8
554.5
538.4
552.9
555.0
558.4
560.3
534.7
545.0
538.0
563.1
553.8
564.6
553.0
548.3
535.1
544.8
548.7