SCHOOL OF DISTANCE EDUCATION
UNIVERSITI SAINS MALAYSIA
JIM 106/4: ELEMENTARY STATISTICS/INTRODUCTION TO STATISTICS
ACADEMIC SESSION 2015/2016
ASSIGNMENT 1
DUE DATE: 14th DECEMBER 2015
ANSWER ALL QUESTIONS.
1.
For each statement, decide whether descriptive or inferential statistics is used.
a.
b.
c.
d.
e.
2.
Classify each as nominal-level, ordinal-level, interval-level, or ratio-level
measurement.
a.
b.
c.
d.
e.
3.
The average life expectancy in New Zealand is 78.49 years.
A diet high in fruits and vegetables will lower blood pressure.
The total amount of estimated losses from hurricane Hugo was $4.2
billion.
Researchers stated that the shape of a persons ears is related to the
persons aggression.
In 2013, the number of high school graduates will be 3.2 million
students.
Rating of movies as G, PG, and R.
Number of candy bars sold on a fund drive.
Classification of automobiles as subcompact, compact, standard, and
luxury.
Temperatures of hair dryers.
Weights of suitcases on a commercial airline.
Classify each variable as discrete or continuous.
a.
b.
c.
d.
e.
Ages of people working in a large factory.
Number of cups of coffee served at a restaurant.
The amount of a drug injected into a guinea pig.
The time it takes a student to drive to school.
The number of gallons of milk sold each day at a grocery store.
4.
In a study of reaction times of dogs to a specific stimulus, an animal trainer
obtained the following data, given in seconds. Construct a histogram, a
frequency polygon, and an ogive for the data; analyze the results.
Class limits
2.32.9
3.03.6
3.74.3
4.45.0
5.15.7
5.86.4
5.
Frequency
10
12
6
8
4
2
The math and reading achievement scores from the National Assessment of
Educational Progress for selected states are listed below. Construct a back-toback stem and leaf plot with the data and compare the distributions.
Math
52
63
55
68
Reading
66
57
59
76
69
59
74
73
62
59
72
61
55
73
65
71
61
77
76
70
69
77
76
70
78
80
66
66
76
67
61
77
6.
Find the mean, median and mode for each set of data in Exercises 4 and 5
above. Is the average about the same for both sets of data?
7.
Find the variance and standard deviation for the two distributions in Exercises
4 and 5 in above. Compare the variation of the data sets. Decide if one data
set is more variable than the other.
8.
In a distribution of 160 values with a mean of 72, at least 120 fall within the
interval 6777. Approximately what percentage of values should fall in the
interval 6282? Use Chebyshevs theorem.
9.
Which score indicates the highest relative position?
a.
b.
c.
A score of 3.2 on a test with X = 4.6 and s = 1.5
A score of 630 on a test with X = 800 and s = 200
A score of 43 on a test with X = 50 and s = 5
10.
Construct a boxplot for the following data which represents the number of
innings pitched by the ERA leaders for the past few years. Comment on the
shape of the distribution.
192
214
228
115
186
238
199
246
238
217
213
234
264
187
11.
In the game of craps using two dice, a person wins on the first roll if a 7 or an
11 is rolled. Find the probability of winning on the first roll.
12.
Elementary and secondary schools were classified by the number of
computers they had.
Computers 110
Schools
3170
1120
4590
2150
16,741
51100
23,753
100+
34,803
Choose one school at random. Find the probability that it has
a.
b.
c.
13.
50 or fewer computers
More than 100 computers
No more than 20 computers
A local postal carrier distributes first-class letters, advertisements, and
magazines. For a certain day, she distributed the following numbers of each
type of item.
Delivered to
Home
Business
First-class letters
325
732
Ads
406
1021
Magazines
203
97
If an item of mail is selected at random, find these probabilities.
a.
b.
c.
The item went to a home.
The item was an ad, or it went to a business.
The item was a first-class letter, or it went to a home.
14. Two dice are rolled. Find the probability of getting
a.
b.
c.
d.
A sum of 5, 6, or 7
Doubles or a sum of 6 or 8
A sum greater than 8 or less than 3
Based on the answers to parts a, b, and c, which is least likely to
occur? Explain why.
15.
A circuit to run a model railroad has 8 switches. Two are defective. If you
select 2 switches at random and test them, find the probability that the second
one is defective, given that the first one is defective.
16.
At a large university, the probability that a student takes calculus and is on the
deans list is 0.042. The probability that a student is on the deans list is 0.21.
Find the probability that the student is taking calculus, given that he or she is
on the deans list.
17.
A medication is 75% effective against a bacterial infection. Find the probability
that if 12 people take the medication, at least 1 persons infection will not
improve.
18.
There are 16 seniors and 15 juniors in a particular social organization. In how
many ways can 4 seniors and 2 juniors be chosen to participate in a charity
event?
19.
How many different ways can a theatrical group select 2 musicals and 3
dramas from 11 musicals and 8 dramas to be presented during the year?
20.
A package contains 12 resistors, 3 of which are defective. If 4 are selected,
find the probability of getting
a.
b.
c.
21.
0 defective resistors
1 defective resistor
3 defective resistors
Find the probability of selecting 3 science books and 4 math books from 8
science books and 9 math books. The books are selected at random.
