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Active Learning Lecture Slides
For use with Classroom Response Systems
Sampling Distributions
7.1 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 © 2013 Pearson Education, Inc.
7.1 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 © 2013 Pearson Education, Inc.
7.2 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 deviation of X (the number 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 © 2013 Pearson Education, Inc.
7.2 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 deviation of X (the number 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 © 2013 Pearson Education, Inc.
7.3 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) 0.006
b) 0.03
c) 0.0901
d) 0.9099
e) 0.9680
Copyright © 2013 Pearson Education, Inc.
7.3 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) 0.006
b) 0.03
c) 0.0901
d) 0.9099
e) 0.9680
Copyright © 2013 Pearson Education, Inc.
7.4 Suppose that 80% of Americans prefer milk
chocolate to dark chocolate. Is the sampling
distribution of the sample proportion that prefers
milk chocolate approximately normally distributed
for samples of size 200?
a) Yes, because n is bigger than 30.
b) Yes, because n is bigger than 15.
c) Yes, because np  15 and n(1  p )  15.
d) No, because np or n(1  p) is not greater than
15.
Copyright © 2013 Pearson Education, Inc.
7.4 Suppose that 80% of Americans prefer milk
chocolate to dark chocolate. Is the sampling
distribution of the sample proportion that prefers
milk chocolate approximately normally distributed
for samples of size 200?
a) Yes, because n is bigger than 30.
b) Yes, because n is bigger than 15.
c) Yes, because np  15 and n(1  p )  15.
d) No, because np or n(1  p) is not greater than
15.
Copyright © 2013 Pearson Education, Inc.
7.5 What is the sampling distribution of the sample
proportion if np  15 and n(1  p)  15 ?
a) Approximately Normal with a mean of p and a
standard error of p(1  p)
n
b) Approximately Normal with a mean of np and
a standard error of np(1  p)
c) Approximately Binomial with a mean of p and
a standard error of p 1  p 
n
d) Approximately Binomial with a mean of np and
a standard error of np(1  p)
Copyright © 2013 Pearson Education, Inc.
7.5 What is the sampling distribution of the sample
proportion if np  15 and n(1  p)  15 ?
a) Approximately Normal with a mean of p and a
standard error of p(1  p)
n
b) Approximately Normal with a mean of np and
a standard error of np(1  p)
c) Approximately Binomial with a mean of p and
a standard error of p 1  p 
n
d) Approximately Binomial with a mean of np and
a standard error of np(1  p)
Copyright © 2013 Pearson Education, Inc.
7.6 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 different
sample means.
Copyright © 2013 Pearson Education, Inc.
7.6 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 different
sample means.
Copyright © 2013 Pearson Education, Inc.
7.7 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 x ?
a) The mean will increase.
b) The mean will decrease.
c) The standard error will increase.
d) The standard error will decrease.
Copyright © 2013 Pearson Education, Inc.
7.7 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 x ?
a) The mean will increase.
b) The mean will decrease.
c) The standard error will increase.
d) The standard error will decrease.
Copyright © 2013 Pearson Education, Inc.
7.8 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 x ?
a) 2,000
b) 2,000 / 40
c) 2,000 / 40
d) 27,000 / 40
Copyright © 2013 Pearson Education, Inc.
7.8 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 x ?
a) 2,000
b) 2,000 / 40
c) 2,000 / 40
d) 27,000 / 40
Copyright © 2013 Pearson Education, Inc.
7.9 Suppose that for people in Idaho the
population mean number of hours worked per
week is 40.2 hrs and the population standard
deviation is 0.4 hrs. Between what two values
will 95% of all sample means from all possible
samples of size 40 lie between?
a) (38.94, 41.47)
b) (39.40, 41.00)
c) (40.07, 40.33)
d) (40.14, 40.26)
Copyright © 2013 Pearson Education, Inc.
7.9 Suppose that for people in Idaho the
population mean number of hours worked per
week is 40.2 hrs and the population standard
deviation is 0.4 hrs. Between what two values
will 95% of all sample means from all possible
samples of size 40 lie between?
a) (38.94, 41.47)
b) (39.40, 41.00)
c) (40.07, 40.33)
d) (40.14, 40.26)
Copyright © 2013 Pearson Education, Inc.
7.10 For which combination of population and
sample size listed below will you find the
sampling distribution of the sample mean
approximately normally distributed?
a) Population is Right Skewed and n = 10
b) Population is Right Skewed and n = 40
c) Population is Bell Shaped and n = 10
d) B and C only
e) A, B and C
Copyright © 2013 Pearson Education, Inc.
7.10 For which combination of population and
sample size listed below will you find the
sampling distribution of the sample mean
approximately normally distributed?
a) Population is Right Skewed and n = 10
b) Population is Right Skewed and n = 40
c) Population is Bell Shaped and n = 10
d) B and C only
e) A, B and C
Copyright © 2013 Pearson Education, Inc.
7.12 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 © 2013 Pearson Education, Inc.
7.12 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 © 2013 Pearson Education, Inc.
7.13 The distribution of textbook sales for all
college students is right (Rt.) 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) Shape: Normal
b) Shape: Approx. Normal
c) Shape: Rt. Skewed
d) Shape: Rt. Skewed
Copyright © 2013 Pearson Education, Inc.
Mean: 300 Stdev: 120
Mean: 300 Stdev: 120 / 40
Mean: 300 Stdev: 120
Mean: 280 Stdev: 109
7.13 The distribution of textbook sales for all
college students is right (Rt.) 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) Shape: Normal
b) Shape: Approx. Normal
c) Shape: Rt. Skewed
d) Shape: Rt. Skewed
Copyright © 2013 Pearson Education, Inc.
Mean: 300 Stdev: 120
Mean: 300 Stdev: 120 / 40
Mean: 300 Stdev: 120
Mean: 280 Stdev: 109
7.14 The distribution of textbook sales for all college students
is right (Rt.) 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) Shape: Approx. Normal
b) Shape: Most likely Rt. Skewed
c) Shape: Most likely Rt. Skewed
d) Shape: Approx. Rt. Skewed
Copyright © 2013 Pearson Education, Inc.
Mean: 300 Stdev: 120 /
Mean: 280 Stdev: 109
Mean: 300 Stdev: 120
Mean: 300 Stdev: 120 /
40
40
7.14 The distribution of textbook sales for all college students
is right (Rt.) 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) Shape: Approx. Normal
b) Shape: Most likely Rt. Skewed
c) Shape: Most likely Rt. Skewed
d) Shape: Approx. Rt. Skewed
Copyright © 2013 Pearson Education, Inc.
Mean: 300 Stdev: 120 /
Mean: 280 Stdev: 109
Mean: 300 Stdev: 120
Mean: 300 Stdev: 120 /
40
40
7.15 The distribution of textbook sales for all
college students is right (Rt.) 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 for a sample of size 40?
a) Shape: Approx. Normal
b) Shape: Approx. Normal
c) Shape: Approx. Normal
d) Shape: Approx. Normal
Copyright © 2013 Pearson Education, Inc.
Mean: 300 Stdev: 120
Mean: 280 Stdev: 109
Mean: 300 Stdev: 120 / 40
Mean: 300 Stdev: 109 / 40
7.15 The distribution of textbook sales for all
college students is right (Rt.) 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 for a sample of size 40?
a) Shape: Approx. Normal
b) Shape: Approx. Normal
c) Shape: Approx. Normal
d) Shape: Approx. Normal
Copyright © 2013 Pearson Education, Inc.
Mean: 300 Stdev: 120
Mean: 280 Stdev: 109
Mean: 300 Stdev: 120 / 40
Mean: 300 Stdev: 109 / 40