Download In Lecture exercises on Sampling Distributions.

Active Learning Lecture Slides
For use with Classroom Response Systems
Chapter 7: Sampling Distributions
Statistics: The Art and
Science of Learning from
Data
Second Edition
by Agresti/Franklin
7.1.1) Suppose that 40% of men over the age of
30 suffer from lower back pain. For a random
sample of 50 men over the age of 30, find the
mean and the standard error of the sampling
distribution of the sample proportion of men over
the age of 30 that suffer from lower back pain.
a) Mean = 0.40
Standard Error = 0.0693
b) Mean= 20
Standard Error = 3.464
c) Mean = 0.40
Standard Error = 3.464
d) Mean = 20
Standard Error = 0.0693
e) Cannot be determined
Copyright © 2009 Pearson Education
7.1.1) Suppose that 40% of men over the age of
30 suffer from lower back pain. For a random
sample of 50 men over the age of 30, find the
mean and the standard error of the sampling
distribution of the sample proportion of men over
the age of 30 that suffer from lower back pain.
a) Mean = 0.40
Standard Error = 0.0693
b) Mean= 20
Standard Error = 3.464
c) Mean = 0.40
Standard Error = 3.464
d) Mean = 20
Standard Error = 0.0693
e) Cannot be determined
Copyright © 2009 Pearson Education
7.1.3) Suppose that a pre-election poll of 500
people showed that 51% of the sample supported
the incumbent senator. If the population proportion
who supported the incumbent senator is really
48%, how likely is it that we would see poll results
such as this or higher?
a)
b)
c)
d)
e)
0.006
0.03
0.0823
0.0901
0.0968
Copyright © 2009 Pearson Education
7.1.3) Suppose that a pre-election poll of 500
people showed that 51% of the sample supported
the incumbent senator. If the population proportion
who supported the incumbent senator is really
48%, how likely is it that we would see poll results
such as this or higher?
a)
b)
c)
d)
e)
0.006
0.03
0.0823
0.0901
0.0968
Copyright © 2009 Pearson Education
7.1.4) Suppose that 80% of Americans prefer milk
chocolate to dark chocolate. Is the sampling
distribution of the sample proportion that prefers
milk chocolate normally distributed for samples of
size 200?
a)
b)
c)
d)
Yes, because n is bigger than 30.
Yes, because n is bigger than 15.
Yes, because np > 15 and n(1-p) > 15.
No, because np or n(1-p) is not greater than 15.
Copyright © 2009 Pearson Education
7.1.4) Suppose that 80% of Americans prefer milk
chocolate to dark chocolate. Is the sampling
distribution of the sample proportion that prefers
milk chocolate normally distributed for samples of
size 200?
a)
b)
c)
d)
Yes, because n is bigger than 30.
Yes, because n is bigger than 15.
Yes, because np > 15 and n(1-p) > 15.
No, because np or n(1-p) is not greater than 15.
Copyright © 2009 Pearson Education
7.1.5) What is the sampling distribution of the
sample proportion if np > 15 and n(1 - p) > 15?
ˆ ~ N (np, np(1  p))
a) p
b) X ~ N ( p,
p(1  p)
)
n
c) pˆ ~ Bin(np, np(1  p))
d)
ˆ ~ N ( p,
p
p (1  p )
n
Copyright © 2009 Pearson Education
)
7.1.5) What is the sampling distribution of the
sample proportion if np > 15 and n(1 - p) > 15?
ˆ ~ N (np, np(1  p))
a) p
b) X ~ N ( p,
p(1  p)
)
n
c) pˆ ~ Bin(np, np(1  p))
d)
ˆ ~ N ( p,
p
p (1  p )
n
Copyright © 2009 Pearson Education
)
7.2.1) Suppose that you and 100 other people ask
25 randomly selected workers how much money
they spent on lunch. Which of the following
statements would be true?
a) All samples would result in the same sample
mean.
b) All samples would results in slightly difference
sample means.
Copyright © 2009 Pearson Education
7.2.1) Suppose that you and 100 other people ask
25 randomly selected workers how much money
they spent on lunch. Which of the following
statements would be true?
a) All samples would result in the same sample
mean.
b) All samples would results in slightly difference
sample means.
Copyright © 2009 Pearson Education
7.2.2) Suppose that you wanted to take a sample of
South Carolina elementary school teachers. What
impact does using a larger sample size have on the
sampling distribution of mean?
a)
b)
c)
d)
The mean will increase.
The mean will decrease.
The standard error will increase.
The standard error will decrease.
Copyright © 2009 Pearson Education
7.2.2) Suppose that you wanted to take a sample of
South Carolina elementary school teachers. What
impact does using a larger sample size have on the
sampling distribution of mean?
a)
b)
c)
d)
The mean will increase.
The mean will decrease.
The standard error will increase.
The standard error will decrease.
Copyright © 2009 Pearson Education
7.2.3) Suppose that South Carolina elementary
school teacher salaries have a distribution that is
right skewed with a mean of $27,000 and a standard
deviation of $2,000. Suppose that someone took a
random sample of 40 elementary school teachers
salaries and found the sample mean. What is the
standard error of mean?
a) 2,000
b) 2,000 / 40
c) 2,000 40
d) 27,000
40
Copyright © 2009 Pearson Education
7.2.3) Suppose that South Carolina elementary
school teacher salaries have a distribution that is
right skewed with a mean of $27,000 and a standard
deviation of $2,000. Suppose that someone took a
random sample of 40 elementary school teachers
salaries and found the sample mean. What is the
standard error of mean?
a) 2,000
b) 2,000 / 40
c) 2,000 40
d) 27,000
40
Copyright © 2009 Pearson Education
7.2.4) Suppose that the population mean
number of hours worked per week for people
from Idaho is 40.2 hrs with a population
standard deviation of 0.4 hrs. Between what
two values will 95% of all sample means from
all possible samples of size 40 lie between?
a)
b)
c)
d)
(38.94, 41.47)
(39.40, 41.00)
(40.07, 40.33)
(40.14, 40.26)
Copyright © 2009 Pearson Education
7.2.4) Suppose that the population mean
number of hours worked per week for people
from Idaho is 40.2 hrs with a population
standard deviation of 0.4 hrs. Between what
two values will 95% of all sample means from
all possible samples of size 40 lie between?
a)
b)
c)
d)
(38.94, 41.47)
(39.40, 41.00)
(40.07, 40.33)
(40.14, 40.26)
Copyright © 2009 Pearson Education
7.2.5) For which combination of population and
sample size listed below will you find the
sampling distribution of the sample mean
normally distributed?
a)
b)
c)
d)
e)
Population is Right Skewed and n = 10
Population is Right Skewed and n = 40
Population is Bell Shaped
and n = 10
B and C only
A, B and C
Copyright © 2009 Pearson Education
7.2.5) For which combination of population and
sample size listed below will you find the
sampling distribution of the sample mean
normally distributed?
a)
b)
c)
d)
e)
Population is Right Skewed and n = 10
Population is Right Skewed and n = 40
Population is Bell Shaped
and n = 10
B and C only
A, B and C
Copyright © 2009 Pearson Education
7.3.1) True or False: For one population
distribution there is only one data distribution.
a) True
b) False
Copyright © 2009 Pearson Education
7.3.1) True or False: For one population
distribution there is only one data distribution.
a) True
b) False
Copyright © 2009 Pearson Education
7.3.2) With larger sample sizes there is a greater
likelihood that the data distribution…
a) will look similar to the population distribution.
b) will look less like the population distribution.
c) is the same as the sampling distribution of the
sample mean.
d) is the same as the sampling distribution of the
sample proportion
Copyright © 2009 Pearson Education
7.3.2) With larger sample sizes there is a greater
likelihood that the data distribution…
a) will look similar to the population distribution.
b) will look less like the population distribution.
c) is the same as the sampling distribution of the
sample mean.
d) is the same as the sampling distribution of the
sample proportion
Copyright © 2009 Pearson Education
7.3.3) The distribution of textbook sales for all
college students is right skewed with a mean of
$300 and a standard deviation of $120. Suppose
that a researcher who didn’t know this information
sampled 40 students. She found that the students
paid $280 on average with a standard deviation
equal to $109. What is the population distribution?
a)
b)
c)
d)
Shape: Normal
Shape: Approx. Normal
Shape: Rt. Skewed
Shape: Rt. Skewed
Mean: 300 Stdev: 120
Mean: 300 Stdev: 120 40
Mean: 300 Stdev: 120
Mean: 280 Stdev: 109
Copyright © 2009 Pearson Education
7.3.3) The distribution of textbook sales for all
college students is right skewed with a mean of
$300 and a standard deviation of $120. Suppose
that a researcher who didn’t know this information
sampled 40 students. She found that the students
paid $280 on average with a standard deviation
equal to $109. What is the population distribution?
a)
b)
c)
d)
Shape: Normal
Shape: Approx. Normal
Shape: Rt. Skewed
Shape: Rt. Skewed
Mean: 300 Stdev: 120
Mean: 300 Stdev: 120 40
Mean: 300 Stdev: 120
Mean: 280 Stdev: 109
Copyright © 2009 Pearson Education
7.3.4) The distribution of textbook sales for all
college students is right skewed with a mean of
$300 and a standard deviation of $120. Suppose
that a researcher who didn’t know this information
sampled 40 students. She found that the students
paid $280 on average with a standard deviation
equal to $109. What is the data distribution?
a)
b)
c)
d)
Shape: Approx. Normal
Shape: Most likely Rt. Skewed
Shape: Approx. Normal
Shape: Approx. Rt. Skewed
Mean: 300 Stdev: 120 40
Mean: 280 Stdev:109
Mean: 300 Stdev: 120
Mean: 300 Stdev: 120 40
Copyright © 2009 Pearson Education
7.3.4) The distribution of textbook sales for all
college students is right skewed with a mean of
$300 and a standard deviation of $120. Suppose
that a researcher who didn’t know this information
sampled 40 students. She found that the students
paid $280 on average with a standard deviation
equal to $109. What is the data distribution?
a)
b)
c)
d)
Shape: Approx. Normal
Shape: Most likely Rt. Skewed
Shape: Approx. Normal
Shape: Approx. Rt. Skewed
Mean: 300 Stdev: 120 40
Mean: 280 Stdev:109
Mean: 300 Stdev: 120
Mean: 300 Stdev: 120 40
Copyright © 2009 Pearson Education
7.3.5) The distribution of textbook sales for all
college students is right skewed with a mean of
$300 and a standard deviation of $120. Suppose
that a researcher who didn’t know this information
sampled 40 students. She found that the students
paid $280 on average with a standard deviation
equal to $109. What is the sampling distribution of
the sample mean?
a)
b)
c)
d)
Shape: Approx. Normal
Shape: Approx. Normal
Shape: Approx. Normal
Shape: Approx. Normal
Mean: 300 Stdev: 120
Mean: 280 Stdev: 109
120
Mean: 300 Stdev:
40
Mean: 300 Stdev: 109 40
Copyright © 2009 Pearson Education
7.3.5) The distribution of textbook sales for all
college students is right skewed with a mean of
$300 and a standard deviation of $120. Suppose
that a researcher who didn’t know this information
sampled 40 students. She found that the students
paid $280 on average with a standard deviation
equal to $109. What is the sampling distribution of
the sample mean?
a)
b)
c)
d)
Shape: Approx. Normal
Shape: Approx. Normal
Shape: Approx. Normal
Shape: Approx. Normal
Mean: 300 Stdev: 120
Mean: 280 Stdev: 109
120
Mean: 300 Stdev:
40
Mean: 300 Stdev: 109 40
Copyright © 2009 Pearson Education