Practice Sheet – 1 Sample Tests
(1) According to the 1990 census, 19.9% of all households in Greensboro consisted of a
“married couple with children.” This year, a researcher took a random sample of 400
households in Greensboro and found that there were 90 households with a “married
couple with children.” Is there a significant difference between this year’s data and
the 1990 data? Test at the 1% level of significance.
(2) Suppose we want to investigate the claim that at least 75% of students attending a
university are opposed to a plan to increase student fees in order to build new parking
facilities. A sample survey reveals 201 of 300 students are opposed. Test the claim
at a 1% level of significance.
(3) The Acme Widget Company produces widgets with an average weight of 120 g. A
quality control technician takes a sample of 64 widgets and finds that the average
weight of widgets in the sample is 117 g with standard deviation of 3 g. Is the
difference significant? Test at the 1% level.
(4) A machine should be set to produce tubes with an average inside diameter of 1.40 cm.
A random sample of 10 tubes is taken and the sample has an average inside diameter
of 1.50 cm with a standard deviation of 0.15 cm. Is the machine set too high? Test at
the 5% level.
(5) A cigarette manufacturer claims its cigarettes have an average nicotine content of 18.3
mg. If a random sample of 7 cigarettes has nicotine contents of 20, 17, 21,19, 22, 21,
and 16 mg, would you agree with the claim? Test at the 5% level.
(6) A certain brand of tire is advertised to have a life of 50,000 miles. After a number of
complaints concerning excessive treadwear for the brand of tire, a consumer testing
group decides to test the company’s claim. They take a random sample of 10 tires
and find an average life of 47,000 miles with a SD of 7,500 miles. Can the consumer
testing group conclude that the company’s advertised claim is false? Test at the 1%
level.
Solution Key for 1 Sample Tests
(1) z  1.3  P  9.5%  there does not seem to be a significant difference between this
year’s data and the 1990 data.
(2) z  3.2  P  .07%  there seems to be significantly fewer than 75% of the
students who oppose the plan.
(3) z  8  P  0%  the difference seems to be significant.
(4) t  2  with df = 9, 2.5% < P < 5%  it seems that the machine is set too high.
(5) t  1.345  with df = 6, 10% < P < 25%  there does not seem to be evidence for
rejecting the claim.
(6) t  1.2  with df = 9, 10% < P < 25%  there is no evidence to conclude that the
claims are false.
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Practice Sheet – 2 Samples and 1 Sample Matched
Difference
(1) In order to test the breaking ability of two types of cars, a simple random of 64 cars
of each type was tested to determine the distance in feet required to stop when
traveling at 40 mph. The findings are shown below:
Average distance for Car A = 118 ft with SD of 10.1 ft
Average distance for Car B = 109 ft with SD of 9.33 ft
Test at the 1% level as to whether the average distance for Car A is longer than that
for Car B.
(2) An educator assigns special activities in addition to regular work to an elementary
class of 18 students to see if it will improve reading abilities. Another class of 20
students follows the same curriculum but does not have the special activities. A test
is given to both classes at the end of 8 weeks. The first class with the special activities
scored an average of 51.48 with SD of 11.01, and the second class without the special
activities scored an average of 41.52 with SD of 17.15. Is the difference in the
average scores significant? Test at the 1% level of significance.
(3) A testing laboratory is testing the life of air conditioning compressors produced by
two different companies. A random sample of 400 units was taken from company A,
and its unit lasted an average of 110 months with SD of 60 months. A random sample
of 100 units was taken from company B, and its unit lasted an average of 90 months
with SD of 40 months. Is the compressor from company A significantly better than
that of company B? Test at the 5% level.
(4) Through random assignment of 200 volunteers with severe migraine headaches, two
groups, A and B, are formed, consisting of 100 people each. A serum is given to
group A but a placebo is given to group B; otherwise, the groups are treated
identically. It is found that 75 subjects in group A and 65 subjects in group B
experience relief within 48 hours. Can you say, at the 5% level of significance, that
the serum is more effective than the placebo in providing relief within 48 hours?
(5) Food Lion advertises that it has lower food prices than Winn Dixie. To test the claim,
Wilson Consumer Testing Company took a random sample of 27 food items that were
common to both stores and got the following:
Food Lion
AV = $1.56
SD = $.85
Winn Dixie
AV = $1.53
SD = $.86
Differences (FL – WD)
AV = $.03
SD = $.12
Do the data seem to substantiate the claim? Test at the 1% level.
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(6) Each summer, Wake Forest has a 4-week program for pre-freshmen who are
interested in medical careers. The federal government requires that we give the
students a pretest and a posttest in mathematics. The following results were
obtained in 1989 and 1990:
1989
Pre
29
35
37
39
40
43
43
1990
Post
42
36
40
41
35
47
42
Pre
33
37
29
39
35
48
25
37
38
64
Post
38
39
33
54
38
53
34
44
41
63
(i) Is there a significant difference between the pretest and the posttest scores in
1989? Test at the 1% level.
(ii) Is there a significant difference between the pretest and the posttest scores in
1990? Test at the 1% level.
(iii)Is the improvement between the pretest and the posttest scores in 1990
significantly better than the improvement between the pretest and the posttest
scores in 1989? Test at the 1% level.
Solution Key for 2 Samples and 1 Sample Matched
Difference
(1) 2 Samples: z  5.23  P  0%  it seems as if the average distance for Car A is
larger than that for Car B.
(2) 2 Samples: z  2.17  P  1.5%  it doesn’t seem that the difference is significant.
(3) 2 Samples: z  4  P  0%  it seems as if the compressors from company A last
longer than those of company B.
(4) 2 Samples: z  1.55  P  6%  serum does not seem to be more effective.
(5) 1 Sample Matched Difference: z  1.3  P  9.5%  the difference does not seem
to be significant.
(6) (i) 1 Sample Matched Difference: t  1.16  with df = 6, 10% < P < 25% 
there doesn’t seem to be significant improvement
(ii) 1 Sample Matched Difference: t  3.74  with df = 9, P < 0.5%  the
improvement seems to be significant.
(iii) 2 Samples: t  1.10  with df = 15, 10% < P < 25%  the improvement in
1990 does not seem to be significantly better than the improvement in 1989.
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Practice Sheet -
2
Tests
(1) A rat was sent down a ramp 90 times. Each time the rat must choose one of three
doors. Doors A, B, and C were chosen 23, 36, and 31 times respectively. Do the data
present sufficient evidence to indicate that some doors are preferred over others?
Test at the 5% level.
(2) In 1981 the AMA published data on the percent of physicians in four major specialty
categories, with the following results: General Practice 14.2%; Medical 30.6%;
Surgical 26.4%; and Other 28.8%. This year a researcher randomly selects 500
physicians currently practicing and asks them about their specialty, with the
following results: 62 are in General Practice; 172 in Medical; 130 in Surgical; and
136 are in Other. Are this year’s results significantly different from those in 1981?
Test at the 5% level.
(3) In the game of chess, the first few moves play a very important role in determining
the final outcome. Five different opening moves are highly favored by experts. To
determine whether one or more of these strategies is most preferred by grandmasters
in international competition, a random sample of 100 grandmasters is taken, and each
is asked which of the opening moves he or she prefers. A summary of the responses
is shown below:
Opening
Ruy Lopez
Queen’s Gambit Declined
Sicilian Defense
French Defense
Queen’s Pawn Game
Frequency
35
25
15
15
10
Test at the 5% level that no preference is shown.
(4) An investigator wishes to study the relationship, if any, between car preference and
geographic region. Two groups are chosen at random, one from the East Coast and
one from the West Coast. Each person is classified as preferring either American or
Japanese or German cars. The results are shown below:
REGION
EAST COAST
WEST COAST
AMERICAN
182
154
JAPANESE
136
215
Test at the 5% level that car preference is independent of region.
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GERMAN
203
110
(5) “Which picture of Elvis should be used on the new postage stamp?” This question
was asked of 200 randomly selected people across the country, giving the following
results:
Young Elvis
Old Elvis
East
26
30
Region
Midwest
18
12
South
58
12
West
30
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Does the preference for a particular Elvis depend on the region of the country? Test
at the 1% level.
(6) An analysis of accident data was made to determine whether the frequency of fatal
accidents was dependent on the size of the car. The data for 346 accidents are as
follows:
Fatal
Non-Fatal
Small
67
128
Size of Car
Medium
26
63
Large
16
46
Test at the 1% level as to whether the incidence of fatality is independent of car size.
Solution Key for
2
Tests
(1) Goodness of Fit:  2  2.87  with df = 2, 10% < P < 30%  there does not seem
evidence to indicate that some doors are preferred over others.
(2) Goodness of Fit:  2  3.98  with df = 3, 10% < P < 30%  the results this year
do not seem to be significantly different from those in 1981.
(3) Goodness of Fit:  2  20  with df = 4, P < 1%  it seems that there is a
preference of opening moves.
(4) Independence of 2 Attributes:  2  46.29  with df = 2, P < 1%  the preference
seems to be dependent on the region.
(5) Independence of 2 Attributes:  2  19.47  with df = 3, P < 1%  the preference
for a particular Elvis seems to be dependent on the region.
(6) Independence of 2 Attributes:  2  2.25  with df = 2, 30% < P < 50%  the
incidence of fatality seems to be independent of car size.
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