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Algebra 2 Trig Honors Notes 11.2
Populations, Samples and Hypothesis
*Statistics is the science of collecting, organizing and interpreting data.
Part I Warm up
1) Describe the sample space for each experiment.
a) One card is drawn from a standard deck of 52 cards.
b) A spinner that contains three colors, red, blue and yellow is spun twice.
c) For one full day, customers at Midway Airport are asked if the wait time
is acceptable.
A population is the collection of all data, such as responses, measurements or
counts.
A sample is a subset of a population. A sample is only a piece of the complete
data.
2) A census consists of data from an entire population. What is a random
sample? Why would we use a random sample instead of obtaining all of the
population data?
3) Determine for each example if the data is collected from a population or a
sample.
a) In the United States, a survey of 2184 adults ages 18 and over found
that 1328 of them own at least one pet.
b) The college degrees of every employee at the hospital.
c) To estimate gas mileage of new cars sold in the United States, a
consumer advocacy group tests 845 new cars and finds they have an
average of 25.1 miles per gallon.
4) Identify the population and sample. Describe the sample.
a) In the United States, a survey of 1000 households with at least one
child found that 874 of them have at least two computers.
b) In a university, a survey of 1641 students found that 479 of them do
not know the name of their college’s mascot.
A parameter is a numerical description of a population characteristic.
A statistic is a numerical description of a sample characteristic.
Why would a statistic be used to estimate a parameter?
4) Determine whether the numerical value is a parameter or a statistic.
a) On a high school football team, 2% of the players are vegetarians.
b) The average amount of the surveyed utility bills is $176.42.
c) For all students taking the SAT in a recent year, the mean
mathematics score was 514. Is the mean score a parameter or a
statistic?
d) A survey of 1060 women, ages 20 – 29 in the United States, found
that the standard deviation of their heights is about 2.6 inches. Is the
standard deviation of the heights a parameter or a statistic?
A hypothesis is a claim about a characteristic of a population. One way to
analyze a hypothesis is to perform a simulation. When the results are
highly unlikely to occur, the hypothesis is probably false.
5)
5 Why is the following an exam
mple of a h
hypothesis?
?
A drug company
c
cllaims that patients ussing its we
eight-loss d
drug lose an average o
of
24 poun
nds in the first
f
three
e months.
6)
6 You roll a die 5 tim
mes and do
o not get ann even num
mber. The probability
y of
5
1
avors odd
this happening is    0.03
3125 , so yoou suspect this die fa
2
numberss. Simulate
e the rollin
ng of the die by repeaatedly draw
wing 200
random samples
s
of
f size 50.
pothesis?
a) Whatt is the hyp
b) Wha
at should yo
ou conclude
e if you roll the die 5
50 times an
nd get 26 o
odd
numb
bers?
ou conclude
e if you rol l the die 50 times an
nd get 35 o
odd
c) Whatt should yo
numb
bers?
Day 4 Homework Worksheet 11.2
Part I: Determine whether the data is collected from a population or a sample.
Explain your reasoning.
1) The address of every student in the school.
2) A survey of 80 people who access a website.
3) The number of high school students in the United States.
4) The color of every third car that passes your house.
5) A survey of 100 fans at the football game with 1800 spectators.
Part II Identify the population and the sample. Explain your reasoning.
6) In an office building, a survey of 648 employees found that 147 of them
ride the subway to work each day.
7) In Florida, a survey of 2500 homeowners found that 1145 of them have
switched their homeowner’s insurance policy to a different company within
the last 3 years.
8) In a school district, a survey of 1,300 high school students found that 1,001
of them like the new healthy food choices in the cafeteria.
Part III
I Determine whethe
er the nume
erical value
e is a param
meter or a statistic.
Explain your reaso
oning.
T
fourr percent of
o the survveyed hock
key playerss first played hockey
9) Thirty
before
b
theiir 10th birthday.
E
o percent of
o all the tiickets sold
d were for the Saturd
day matine
ee.
10) Eighty-two
S
ree percen
nt of all of the students in a school would prefer to
11) Seventy-th
have school dances on
n a Saturda
ay.
12) A survey of
f U.S. adults found that 10% be
elieve a cle
eaning prod
duct they u
use
iss not safe for
f the envvironment.
Part IV Analyzing a hypothesis.
13) You
Y flip a coin
c
4 time
es and do no
ot get tailss. You susp
pect this c
coin favors
heads. You simulate flipping
f
the
e coin 50 tiimes by repeatedly d
drawing 200
0
ra
andom sam
mples of siz
ze 50. The
e histogram
m shows the results.
a) What
W
is your hypothe
esis?
b) What
he actual ccoin 50 tim
W
should you conc
clude when
n you flip th
mes and gett 27
heads?
W
should you conclude when you flip th
he actual co
oin 50 time
es and get 33
c) What
heads?