Download Mathematics 2204 Final Review Chapter 5 Statistics

Mathematics 2204
Final Review
Chapter 5
1.
Statistics
To find the average weight of players in the National Football League, Susan randomly
selects one team and then finds the average weight of all players on that team. What kind
of sampling method was used?
(A)
(C)
2.
Cluster
Stratified
(B)
(D)
Simple Random
Systematic
The life expectancy of a washing machine is normally distributed with a mean of 7 years and
a standard deviation of 1.5 years. What percentage of washing machines is expected to last
between 4 and 10 years?
(A) 34.0%
3.
(B)
47.5%
(C)
68.0%
(D)
95.0%
Sheila randomly selects 50 people and asks how many hours in a week they watch
television. She calculates her 95% confidence interval to be 5.659,6.341 . What was the
mean number of hours of her sample of 50 people?
(A)
4.
0.341
(B)
5.659
(C)
6.000
(D)
6.341
According to the histogram, what percentage of families uses public transportation more
than 3 times a week?
Number of Times Families Use Public Transportation Per Week
30
10
12
15
18
25
20
Frequency
(A)
(B)
(C)
(D)
15
10
5
0
0
5.
1
2
3
Number of Times per week
4
Tracey is creating a 95% confidence interval. Which of the following sample sizes will create
the smallest confidence interval?
(A)
6.
100
(B)
200
(C)
300
(D)
400
A sample of 30 bags of potato chips is collected. The bags are opened and the number of
chips in each bag is recorded. It is determined that the average number of chips per bag is
40.5 with a standard deviation of 4.9. If a 95% confidence interval is to be created, what is
the margin of error?
(A)
0.32
(B)
1.47
(C)
1.75
(D)
2.29
5 or more
7.
Which of the following would typically result in producing a biased sample from a
population of 10000 people?
(A)
(B)
(C)
(D)
8.
9.
Asking people if they want to be a member of the sample, and selecting
those people who want to be a member.
Making a list of every person’s name in alphabetical order, randomly
selecting a number n, and selecting every nth person to be a part of the
survey.
Randomly selecting a letter and selecting every person in the population
whose last name begins with that letter.
Writing each person’s name on a sheet of paper, placing the sheets in a hat,
and then randomly picking 50 pieces of paper.
Which of the following normal distributions has the smallest standard deviation?
Tracey is creating a 95% confidence interval. Which of the following sample sizes will create the
smallest confidence interval?
(A)
100
(B)
200
(C)
300
(D)
400
10.
A sample of 30 bags of potato chips is collected. The bags are opened and the number of chips
in each bag is recorded. It is determined that the average number of chips per bag is 40.5 with a
standard deviation of 4.9. If a 95% confidence interval is to be created, what is the margin of
error?
(A)
0.32 (B)
1.47 (C)
1.75 (D)
2.29
11.
Which of the following would typically result in producing a biased sample from a population of
10000 people?
(A)
(B)
(C)
(D)
Asking people if they want to be a member of the sample, and selecting
those people who want to be a member.
Making a list of every person’s name in alphabetical order, randomly selecting
a number n, and selecting every nth person to be a part of the survey.
Randomly selecting a letter and selecting every person in the population
whose last name begins with that letter.
Writing each person’s name on a sheet of paper, placing the sheets in a hat,
and then randomly picking 50 pieces of paper.
12.
Which of the following histograms has the smallest standard deviation?
B)
18
16
14
12
10
8
6
4
2
5
10
15
20
25 30
Bins
35
40
45
50
C)
5
10
15
20
25 30
Bins
10
15
20
25 30
Bins
35
40
45
40
45
50
50
D)
18
16
14
12
10
8
6
4
2
Frequency
Frequency
18
16
14
12
10
8
6
4
2
Frequency
Frequency
A)
5
10
15
20
25 30
Bins
35
40
45
50
18
16
14
12
10
8
6
4
2
5
35
13. In order to determine the level of student satisfaction with the cafeteria food at her
high school, Mary asked six of her friends for their opinions. What sampling
technique did Mary use?
A) Convenience Sampling
C) Stratified Random Sampling
B) Simple Random Sampling
D) Systematic Sampling
14. George is interested in finding out what percentage of the 900 students in his school
have cell phones. Which of the following samples would give him the best estimate?
A) Surveying 30 of his friends.
B) Surveying 38 students in his Math 2204 class.
C) Surveying every tenth student as they leave the school for the day.
D) Surveying every second student entering the library at lunch hour one day.
15. The average amount of soap used daily by a car wash terminal for the past 5 years is
is normally distributed. The average amount of soap used daily is 150 kg and 68% of
the soap used is between 130 kg and 170 kg. What is the standard deviation for the
daily amount of soap used?
A) 5 kg
B) 10 kg
C) 20 kg
D) 40 kg
16. A random sample of 80 hockey players was taken from the National Hockey League.
The average age of the sample was 30 years with a standard deviation of 1.5 years.
What is the 95% confidence interval?
A) Between 29.57 and 30.43 years.
C) Between 29.73 and 30.27 years.
B) Between 29.67 and 30.33 years.
D) Between 30.57 and 32.43 years.
17. A sample of 40 math students is selected from Level II . The average score on there
Unit 5 test was 72 percent with a standard deviation of 6 percent. If a 95%
confidence interval is to be created, what is the margin of error?
A) 0.95
B) 1.56
C) 1.86
D) 2.43
18. Some scientists believe that a new drug would benefit about half of the people
with a certain blood disorder. To estimate the proportion of patients who would
benefit from taking the drug, the scientists administered it to a random sample of
patients who have the blood disorder. If a 95% confidence interval is created which
sample size will create the smallest confidence interval?
A) 50 patients
B) 100 patients
C) 1500 patients
D) 3000 patients
PART II:
1. The life expectancy of a certain brand of hair dryer is known to be normally
distributed with a mean of 3 years and a standard deviation of 0.75 years. A
company produces 3000 of these hair dryers. Draw and label a normal
distribution curve and determine how many hair dryers are expected to last
more than 1.5 years.
2.
A soft drink manufacturer advertises that a certain size of its diet cola has a
mean weight of 591 grams. A random sample of 50 bottles is selected. The
sample mean is 589.3 grams and the sample standard deviation is 13.7 grams.
Algebraically determine the 95% confidence interval. Does the confidence interval
support the company’s claim?
3.
A factory has 2200 workers with a mean weekly salary of $650. A simple
random sample of 250 of these workers is selected. The sample has a mean
weekly salary of $630 with a standard deviation $40. Algebraically calculate
the 95% confidence interval.
4.
The speed limit for vehicles crossing the Pinware River bridge is 60 km/h.
The speed of 20 000 vehicles crossing the bridge is normally
distributed with an average speed of 68 km/h and a standard deviation of
8 km/h. Draw and label a normal distribution curve and determine what
percent of the vehicles are travelling over the speed limit of 60 km/h.
5.
Good Day Tires claims that their new line of tires will last for 80000 km. A consumer research
group decides to test this claim. The group randomly selects 400 tires and tests each tire. The
data from this sample shows that the mean life of a tire is 78000 km, with a standard deviation
of 1500 km.
(A)
(B)
6.
Algebraically determine the 95% confidence interval for the mean life of a tire.
Does the confidence interval support the claim of Good Day Tires? Explain your answer.
The number of chocolate chips in a certain brand of chocolate chip cookies is known to be
normally distributed with a mean of 15 chips per cookie and a standard deviation of 1.5. Draw
and label a normal distribution curve for this situation, and determine the percentage of cookies
has between 12 and 16.5 chocolate chips.