Ch 21 Practice/Homework
Name _____________
Math 207: Intro to Stats
Practice Chapter 21
1. In the example from your notes about the college students living at home:
a. the 317 is the __________value for the number of students in the sample who
were living at home (expected or observes)
. The SD of the box is _______0.41 (exactly equal to or estimated from the data)
c. The SE for the number of students in the sample who were living at home is
________ (exactly equal to or estimated from the data as)
2. A simple random sample of size 400 was taken from the population of all manufacturing
establishments in a certain state; 11 establishments in the sample had 100 employees
or more. Estimate the percentage of manufacturing establishments with 100 employees
or more. Attach a standard e
or to the estimate.
3. Suppose there is a box of 100,000 tickets each marked as 0 or 1. Suppose that in fact,
20% of the tickets in the box are 1’s. Calculate the standard e
or for the percentage of
1’s in 400 draws from the box.
4. Three different people take simple random samples of size 400 from the box in problem
#3 without knowing its contents. The number of 1’s in the first sample is 72, in the
second , it is 84 and in the third it is 98. Each person estimates the SE by the bootstrap
method.
a. The first person estimates the percentage of 1’s in the box as _______and
figures this estimate is likely to be off by ______or so.
. The second person estimates the percentage of 1’s in the box as _______and
figures this estimate is likely to be off by ______or so.
c. The third person estimates the percentage of 1’s in the box as _______and
figures this estimate is likely to be off by ______or so.
5. Refer to # 3 and 4 data, Compute a 95% confidence interval for the percentage of 1’s in
the box, using the data obtained by the person in exercise 4A. Repeat for the other 2
people. Which of the three intervals cover the population percentage, that is, the
percentage of 1’s in the box? Which do not? Remember they do not know the contents
of the box but you do.
6. Probabilities are used when reasoning from the _______to the ________; confidence
levels are used when reasoning from the ________to the _____________
7. The chance e
or is in the ________value. The confidence interval is for the
_______percentage.
8. A box contains a large number of red and blue ma
les; the proportions of red ma
les is
known to be 50%. A simple random sample of 100 ma
les is drawn from the box. Say
whether each of the following statements is true or false and explain why.
a. The percentage of red ma
les in the sample has an expected value of 50%, and
an SE of 5%.
. The 5% measures the likely size of the chance e
or in the 50%.
c. The percentage of reds in the sample will be around 50% give or take 5% of so.
d. An approximate 95% confidence interval for the percentage of reds in the sample
is 40% to 60%.
e. There is about a 95% chance that the percentage of reds in the sample will be in
the range from 40% to 60%.
CH 20 Practice/Homework
Name ___________
Math 207 Intro to Stats
Practice Chapter 20
1. A town has 30,000 registered voters, of whom 12,000 are Democrats. A survey
organization is about to take a simple random sample of 1000 registered voters. A box
model is used to work out the expected value and the SE for the percentage of
Deomocrats in the sample. Match each phrase on list A with a phrase or a number on
list B (items on list B may be used more than once, or not at all)
List A List B
population Number of 1’s among the draws
Population percentage Percentage of 1/s among the draws
sample 40%
Sample size box
Sample number draws
Sample percentage 1000
Denominator for sample percentage 12,000
2. A coin will be tossed 10,000 times. Match the SE with the formula. (one formula will be
left over)
SE for the….. Formula
Percentage of heads 10000 × 50%
Number of heads 50
10000 × 100%
10000 × 0. 5
3. The box [ XXXXXXXXXX] has an average of 0.6 and the SD of 0.8. True or False: The SE fo
the percentage of 1’s in 400 draws can be found as follows: Justify your answers.
SE for number of 1’s = 400 × 0. 8 = 16
SE for percent of 1’s = 16400 × 100% = 4%
4. You are drawing at random from a large box of red and blue ma
les. Fill in the blanks:
a. The expected value for the percentage of reds in the ____________ equals the
percentage of reds in the _______________.
. As the number of draws goes up, the SE for the _____________of reds in the
sample goes up but the SE for the _____________of reds goes down.
5. According to the Census, a certain town has a population of 100,000 people ages 18
and over. Of them, 60% are ma
ied, 10% have incomes over $75,000 a year, and 20%
have college degrees. As part of a pre-election survey, a simple random sample of 1600
people will be drawn from this population.
a. To find the chance that 58% or less of the people in the sample are ma
ied, a
ox model is needed. Should the number of tickets in the box be 1600, o
100,000? Explain. Then find the chance.
. To find the chance that 11% or more of the people in the sample have incomes
over $75,000 a year, a box model is needed. Should each ticket in the box show
the person’s income? Explain. Then find the chance.
c. Find the chance that between 19% and 21% of the people in the sample have a
college degree.
6. You have hired a polling organization to take a simple random sample from a box of
100,000 tickets, and estimate the percentage of 1’s in the box. Unknown to them the box
contains 50% 0’s and 50% 1’s. How far off should you expect them to be:
a. If they draw 2500 tickets?
. If they draw 25,000 tickets?
c. If they draw 100,000 tickets?
Practice/Homework for Chapter 19
Name _________________
Math 207 Intro to Stats
Practice/Homework Ch 19
Answer the following questions based off the class discussion on Chapter 19:
1. A survey is ca
ied out at a university to estimate the percentage of undergraduates
living at home during the cu
ent term.
a. a) What is the population?
. b) What is the parameter?
2. The registrar keeps an alphabetical list of all undergraduates, with their cu
ent
addresses. Suppose there are 10,000 undergraduates in the cu
ent term. Someone
proposes to choose a number at random from 1 to 100, count that far down the list,
taking that name and every 100th name after it for the sample.
a. Is this a probability method? Justify your answe
. Is it the same as simple random sampling? Justify your answer.
c. Is there selection bias in this method of drawing a sample? Justify your answer.
3. In the Netherlands, all men take a military pre-induction exam at age 18. The exam
includes an intelligence test known as “Raven’s progressive matrices” and includes
questions about demographic variables like family size. A study was done in 1968,
elating the test scores of 18-year old men to the number of their
others and sisters.
The records of all the exams taken in 1968 were used.
a. What is the population?
. What is the sample?
c. Is there any sampling e
or? Justify your answer.
4. Polls often conduct pre-election surveys by telephone (land/cell).
a. Could this bias the results? Justify your answe
. What if the sample is drawn from the telephone book or random generated
google list?
5. Determine if the following are (a) probability methods (b) if they are clusters, simple
andom , quota or just convenience sampling methods and (c) is there any selection bias
a. A completely random method is used to select 75 students. Each undergraduate
student in the fall semester has the same probability of being chosen at any
stage of the sampling process.
. An administrative assistant is asked to stand in front of the li
ary one
Wednesday and to ask the first 100 undergraduate students he encounters what
they paid for tuition the Fall semester. Those 100 students are the sample.
c. The freshman, sophomore, junior, and senior years are number one, two, three
and four, respectively. A random number generator is used to pick two of those
years. All students in those two years are in the sample.
d. Undergraduate students are organized by certain categories (ex: race, sex,
major, etc.). The survey required 3 members from each of the categories to be
interviewed by the school newspaper. The newspaper writers determine who
they will survey to collect their data.