Download Chapter 6 - Practice Problems 3

Chapter 6 - Practice Problems 3
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
1) The weights of five players on a football team are shown below.
Player A B C D E
Weight (lb) 290 310 250 255 220
Consider these players to be a population of interest. The mean weight, μ, for the population is
265 pounds. Construct a table which shows all of the possible samples of size two. For each of the
possible samples, list the players in the sample, their weights, and the sample mean. The first line
of the table is shown below.
Sample Weights x
A,B 290, 310 300
Use your table to find the probability that, for a random sample of size two, the sample mean
will equal the population mean.
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1)
Draw the specified dotplot.
2) The heights (in inches) of 5 players on a basketball team are given in the table.
Player
A B C D
Height (inches) 65 78 72 68
2)
E
57
Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the requested probability.
3) The table reports the distribution of pocket money, in bills, of the 6 students in a statistics seminar.
3)
Student
Hannah Ming Keshaun Tameeka Jose Vaishali
Amount, in dollars
2
4
4
5
5
7
For a random sample of size two, find the probability, expressed as a percent rounded to the nearest
tenth, that the sample mean will be within $1 of the population mean.
A) 80.0%
B) 73.3%
C) 78.6%
D) 66.7%
4) The test scores of 5 students are under consideration. The following is the dotplot for the sampling
distribution of the sample mean for samples of size 2.
4)
Find the probability, expressed as a percent, that the sample mean will be equal to the population mean.
A) 30%
B) 5%
C) 10%
D) 20%
5) The test scores of 5 students are under consideration. The following is the dotplot for the sampling y
distribution of the sample mean for samples of size 2.
Find the probability, expressed as a percent, that the sample mean will be within 1 point of the
population mean.
A) 5%
B) 10%
C) 20%
D) 22%
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5)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
6) The weights of five players on a football team are shown below.
Player A B C D E
Weight (lb) 290 310 250 255 220
6)
Consider these players to be a population of interest. The table below shows all of the possible
samples of size three. For each of the possible samples, the players in the sample, their weights,
and the sample mean are listed.
Sample Weights
x
A, B, C 290, 310,250 283.3
A, B, D 290, 310, 255 285
A, B, E 290, 310 220 273.3
A, C, D 290, 250, 255 265
A, C, E 290, 250, 220 253.3
A, D, E 290, 255, 220 255
B, C, D 310, 250, 255 271.6
B, C, E 310, 250, 220 260
B, D, E 310, 255, 220 261.6
C, D, E 250, 255, 220 241.6
Use the table to find the mean of the variable x.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
For samples of the specified size from the population described, find the mean and standard deviation of the sample mean x.
7) The mean and the standard deviation of the sampled population are, respectively, 113.9 and 32.1.
7)
n = 64
A) μ = 243.7; σ = 2.3
x
x
C) μ = 4.0; σ = 113.9
x
x
B) μ = 113.9; σ = 4.0
x
x
D) μ = 32.1; σ = 4.0
x
x
8) The National Weather Service keeps records of snowfall in mountain ranges. Records indicate that in a
certain range, the annual snowfall has a mean of 97 inches and a standard deviation of 16 inches.
Suppose the snowfalls are sampled during randomly picked years. For samples of size 64, determine the
8)
mean and standard deviation of x.
A) μ = 97; σ = 16
x
x
C) μ = 2; σ = 97
x
x
B) μ = 16; σ = 97
x
x
D) μ = 97; σ = 2
x
x
TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false.
Provide an appropriate response.
9) The mean height for a population is 65 inches and the standard deviation is 3 inches. Let x denote the
mean height for a sample of people picked randomly from the population. True or false, the standard
deviation of x for samples of size 30 is greater than the standard deviation of x for samples of size 20?
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9)
10) The mean height for a population is 65 inches and the standard deviation is 3 inches. Let A and B denote
the events described below.
10)
Event A: The height of a randomly selected person will be 5 inches or further from the population mean.
Event B: The mean height of a random sample of 16 people will be 5 inches or further from the
population mean.
True or false, the probability of event A is greater than the probability of event B?
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Identify the distribution of the sample mean. In particular, state whether the distribution of x is normal or approximately
normal and give its mean and standard deviation.
11)
11) The weights of people in a certain population are normally distributed with a mean of 153 lb and a
standard deviation of 23 lb. Determine the sampling distribution of the mean for samples of size 5.
A) Approximately normal, mean = 153 lb, standard deviation = 4.6 lb
B) Approximately normal, mean = 153 lb, standard deviation = 10.29 lb
C) Normal, mean = 153 lb, standard deviation = 23 lb
D) Normal, mean = 153 lb, standard deviation = 10.29 lb
12) The mean annual income for adult women in one city is $28,520 and the standard deviation of the
incomes is $5000. The distribution of incomes is skewed to the right. Determine the sampling
distribution of the mean for samples of size 43.
12)
A) Approximately normal, mean = $28,520, standard deviation = $762
B) Normal, mean = $28,520, standard deviation = $762
C) Normal, mean = $28,520, standard deviation = $116
D) Approximately normal, mean = $28,520, standard deviation = $5000
Find the indicated probability or percentage for the sampling error.
13) Scores on an aptitude test are normally distributed with a mean of 220 and a standard deviation of 10.
Determine the percentage of samples of size 25 that have a mean score within 3 points of the population
mean score of 220.
A) 38.30%
B) 93.32%
C) 86.64%
D) 13.36%
14) The monthly expenditures on food by single adults living in one neighborhood of Los Angeles are
normally distributed with a mean of $410 and a standard deviation of $75. Determine the percentage of
samples of size 9 that have mean expenditures within $20 of the population mean expenditure of $410.
A) 91.92%
B) 57.62%
C) 98.36%
B) 0.762
C) 0.135
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14)
D) 21.28%
15) Scores on an aptitude test are normally distributed with a mean of 220 and a standard deviation of 30.
What is the probability that the sampling error made in estimating the population mean by the mean of a
random sample of 50 test scores will be at most 5 points?
A) 0.881
13)
D) 0.999
15)
Provide an appropriate response.
16) The mean annual income for adult women in one city is $28,520 and the standard deviation of the
incomes is $5,190. The distribution of incomes is skewed to the right. For samples of size 30, which of the
following statements best describes the sampling distribution of the mean?
16)
A) x is approximately normally distributed.
B) Nothing can be said about the distribution of x.
C) The distribution of x is skewed to the right.
D) x is normally distributed.
17) For the population of one town, the number of siblings is a random variable whose relative frequency
17)
histogram has a reverse J-shape. Let x denote the mean number of siblings for a random sample of size
30. For samples of size 30, which of the following statements concerning the sampling distribution of the
mean is true?
A) x is normally distributed.
B) The distribution of x has a reverse J-shape.
C) x is approximately normally distributed.
D) None of the above statements is true.
Solve the problem.
18) The Central Limit Theorem says the sampling distribution of the sample mean is approximately normal
under certain conditions. What is a necessary condition for the Central Limit Theorem to be used?
18)
A) The population size must be large (e.g., at least 30).
B) The population from which we are sampling must not be normally distributed.
C) The population from which we are sampling must be normally distributed.
D) The sample size must be large (e.g., at least 30).
19) Which of the following statements about the sampling distribution of the sample mean is incorrect?
19)
A) The standard deviation of the sampling distribution is σ.
B) The mean of the sampling distribution is μ.
C) the sampling distribution is approximately normal whenever the sample size is sufficiently large (n
≥ 30).
D) The sampling distribution is generated by repeatedly taking samples of size n and computing the
sample means.
TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false.
For the question below, answer True or False
20) As the sample size taken gets larger, the standard error of the mean gets larger as well.
21) The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large.
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20)
21)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
22) The amount of soda a dispensing machine pours into a 24-ounce can of soda follows a normal
distribution with a mean of 24.03 ounces and a standard deviation of 0.01 ounces. Suppose the quality
control department at the soda plant sampled 100 sodas and found the average amount of soda in the
cans was 24 ounces of soda. What should the quality control department recommend to the management
of the plant?
A) The dispensing machine should be stopped and checked because the results of this sample indicate
the machine specifications are not correct.
B) The machine should continue to operate as this mean is expected given the dispensing machineʹs
specifications.
C) Neither of these recommendations is appropriate as this sample information tell us nothing
concerning the population specifications of the dispensing machine.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
23) The amount of time it takes a student to walk from her home to class has a skewed right
distribution with a mean of 16 minutes and a standard deviation of 1.6 minutes. If data were
collected from 30 randomly selected walks, describe the sampling distribution of x, the sample
mean time.
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23)
22)
Answer Key
Testname: CH 6 SET 3
1)
Sample Weights x
A,B 290, 310 300
A,C 290, 250 270
A,D 290, 255 272.5
A,E 290, 220 255
B,C 310, 250 280
B,D 310, 255 282.5
B,E 310, 220 265
C,D 250, 255 252.5
C,E 250, 220 235
D,E 255, 220 237.5
Probability sample mean equals population mean = 0.1
2)
3) B
4) D
5) C
6) 265 pounds
7) B
8) D
9) FALSE
10) TRUE
11) D
12) A
13) C
14) B
15) B
16) A
17) C
18) D
19) A
20) FALSE
21) FALSE
22) A
23) By the Central Limit Theorem, the sampling distribution of x is approximately normal with μx = μ = 16 minutes and σx =
1.6
σ
= = 0.2921 minutes.
30
n
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