Unit 9 Closure (Review)
CL 9-112. Stephanie is interested in laws concerning the death penalty. She gives the following survey question to her government
class.
“The constitution allows individual states the freedom to enact laws which are not contradictory to federal laws. For example, capital
punishment is permissible in some states but not in others. Are you in favor of the U.S. Congress passing legislation to override every
individual state law and ban the practice of capital punishment?"
Thirty-eight percent of the students respond in favor of a federal law governing the use of capital punishment. Stephanie concludes
that there is insufficient popular support to pass a federal law banning capital punishment.
a) Is 38% a parameter or statistic? How do you know? What population is Stephanie making her conclusion about?
b) What sources of bias are present in the wording of her question?
c) What sampling technique did Stephanie use and how might it introduce bias into her conclusion?
CL 9-113. Suppose Stephanie wanted to determine whether students in her ceramics class have a significantly different opinion
towards capital punishment legislation than those in her government class. She finds 55% of the ceramics students in favor of federal
oversight of capital punishment and concludes that taking ceramics causes opposition to the death penalty. Why is her conclusion
unreasonable? Design an experiment that would test her conclusion.
CL 9-114. It is inventory time at the Mathletes Shoe Super Store. To speed up the process, Iris, the storeowner, decided to find the
value of the inventory by counting the number of pairs of shoes that belong in $30 intervals. She made the following table:
a) Make a relative frequency histogram of the distribution of shoes in the store.
b) Which intervals contain the median, the first quartile and third quartile?
c) Describe the distribution of shoe values in terms of center, shape, spread and outliers.
d) What proportion of shoes are valued at least $150?
e) Calculate an estimated proportion of shoes that cost between $50 and $100.
f) Calculate an estimated mean price for a pair of shoes. Assume every pair of shoes in each dollar interval is valued at the middle
price for that interval.
CL 9-115. Park rangers study the pellets of hawks to determine their eating habits. Hawks regurgitate the indigestible portion of their
diet in a pellet. Pellets are about one or two inches long, and can contain the bones, fur, feathers, and claws of their prey.
In order to determine if hawks were changing their diet to cope with a particularly harsh winter, rangers collected a random sample of
ten pellets. The rodent bones in the pellets had mass: 7.3, 12.1, 4.1, 11.9, 6.3, 4.9, 10.7, 6.3, 0.0, 7.0 grams.
From the sample park rangers will make predictions for the population using a normal model. What is the mean and standard
deviation they will use in their model? Use an appropriate precision in your response based on the precision of the data.
CL 9-116. Consider the Integral Zero Theorem (See Polynomial Theorem Toolkit)
a) Using only integers, list all the possible linear factors of (x3+ 8).
b) Is (x + 8) a factor of (x3+ 8)? Is (x + 2) a factor of (x3+ 8)? Show how you know without graphing.
CL 9-117. Solve the system of equations.
𝑥 𝑦
+ =1
4 3
𝑦
2𝑥 − = 17
3
CL 9-118. Use the graph below to solve 2x+ 1 < 3x.
CL 9-119. Check your answers using the key. Which problems do you feel confident about? Which problems were hard? Have you
worked on problems like these in math classes you have taken before? Use the table to make a list of topics you need help on and a
list of topics you need to practice more.
Answers and Support for Unit 9 Closure
Note: MN = Math Note, LL = Learning Log
Problem
Solutions
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CL 9-112.
a. 38% is a statistic because it represents the opinions of the sample, her
government class. Her conclusion is making a statement about the voting
U.S. population.
b. Stephanie’s question has a lead-in statement about the constitution, which
may persuade survey-takers that states should be allowed to determine
whether or not to use capital punishment.
c. Stephanie probably used a convenience sample because it was easy to
survey those in her government class. Those students have many things in
common like age, location, and level of education, and so do not represent
the U.S. population as a whole. Because they are in a government class, they
may be more aware of state rights versus federal authority.
Lessons 9.1.1,
9.1.2,
and 9.1.3
MN: 9.1.1
Problems 9-22, 923, 9-36, 9-37, 938, 9-50,9-51, 9-62,
and 9-75
CL 9-113.
Stephanie is using samples from her high school that are not representative of Lessons 9.2.1
a larger population. Also, it is likely that students choose for themselves
and 9.2.2
whether or not to take ceramics so it is plausible that the kind of student who MN: 9.2.1
likes ceramics is already opposed to the death penalty rather than ceramics
changing the political opinions of students. To demonstrate cause and effect,
Stephanie would need to take a group of student volunteers and randomly
assign them to government or ceramics courses. After the course is
completed, she could poll them about capital punishment and compare the
results.
CL 9-114.
Problems 9-63, 9-76,
and 9-89
Lesson 9.3.1
Problems 9-72, 973, 9-88, 9-103,
and 9-104
Problems 952 and 9-70
Problems 9-65, 9-73,
and 9-103
b. Q1 $30–60, Med $60–90,
Q3 $90–120c.
c. The distribution is positive or right skewed so the median and IQR would
describe the center and spread. You would need the actual data points to find
these values precisely but the center is approximately $65 and the IQR is
about $60. There are no gaps or outliers.
d. (6 + 4 + 2) / 250 = 0.048 or 4.8%
e. Using one third of the $30-60 interval and one third of the $90-120 interval
((1/3)67 + 60 + (1/3)46) / 250 = 0.391 or 39.1%
f. $15(47) + $45(67)+ $75(60) + $105(46) + $135(18) + $165(6) + $195(4) +
$225(2) / 250 = $70.8
CL 9-115.
Mean 7.1 g, sample standard deviation 3.8 g (not population standard
deviation 3.6 g).
CL 9-116.
a.(x ± 1)(x ± 2), (x ± 4), (x ± 8)
b. (x + 8) is not a factor, (x + 2) is a factor. Use the Remainder
Theorem and determine whether −8 and −2 are zeros. Or, divide
and see that (x + 8) is not a factor because there is a
remainder. (x + 2) is a factor because there is no remainder.
Lesson 8.3.2
MN: 8.3.2
Problems 8-125, 8-138,99, 9-39, and 9-68
CL 9-117.
(8, −3)
Lesson 4.1.1
LL: 4.1.1
Problems 8-11 and 9-26
CL 9-118.
x>1
Lesson 4.2.3
MN: 4.2.3 and 4.2.4
Problems 7-28, 8-41, 8-89,
and 9-91