Essential Statistics
5.1 Review
Name: _______________________________________
1. Sampling students You want to determine whether students at your school think that
teachers are sufficiently available to students outside the classroom. You have the
resources to contact about 200 students.
(a) Specify the population and parameter of interest.
(b) Describe your sample design. For example, will you use a stratified sample
with men and women as strata?
(c) Briefly discuss the practical difficulties that you anticipate. For example, how
will you contact the students in your sample?
(d) What specific question or questions will you ask?
2. Sampling library books A group of librarians wants to estimate what fraction of books
in large libraries falls in each of four height categories. This information will help them
plan shelving. To obtain it, they plan to measure all of the several hundred thousand
books in one library. Describe a sampling design that will save the librarians time and
money.
3. Many popular entertainment shows, such as American Idol and Dancing with the Stars
have an audience-voting component. After evening’s performances, members of the
viewing audience are invited to register their vote for their favorite performer(s) by
calling or texting "900" phone numbers. Calling one number would register their vote for
performer A, another number for performer B, etc. Each call or text will cost the voter
some amount of money. The results of the voting are reported on the following week’s
broadcast. Give one reason why the results are likely to be biased.
4. Many sample surveys are gathered by calling residential phone numbers at random. They
often times ask to speak to someone over the age of 18 whose birthday is closest to
today’s date. Why is this method a good idea?
Essential Statistics
5.1 Review
Name: _______________________________________
5. The faculty disciplinary committee at a local school specifies that a 5-member hearing
panel shall be drawn at random from the 30-member faculty. The school intends to draw
an SRS of size 5 from the following list of faculty.
Abel Adler Calderon
DeVito
Eisinger
Ewbank
Foley
Gonzales
Hay
Ismail
Kirby
Levy
Lowe
Martinez
Miller
Mork
Perrucci
Rothenberg Santogrossi
Schrag
Staaks
Steer
Targ
Toal
Walther
Weinstein
Winer
Wu
Young
Zhang
(a) Tell the school how to go about obtaining an SRS of 5 faculty members using the
partial random digits table below. Be very specific so they can follow your instructions
with ease.
(b) Use the partial table of random digits below to select an SRS of 5 faculty members by
using the method you described in part (a). Mark directly on the table to show your
process clearly.
08421 44753 77377 28744 75592 08563 79140 92454
27816 78416 18329 21337 35213 37741 04312 68508
6. Over-loaded trucks are problematic in that they tend to cause more wear-and-tear on
highways which are designed to carry certain maximum loads. Along many major
highways, such as the Interstate Highway system, are Weight Stations where long-haul
trucks, such as the big 18-wheelers, must pull off the highway when the sign is flashing,
stop and be weighed to make sure they don’t exceed state limits. Highway officials want
to make an estimate of the number of trucks that are over-loaded.
(a) Explain why it would be difficult for state highway officials to take a SRS of trucks to
be weighed on a certain day.
(b) Suppose it takes 20 minutes to accomplish each weigh-in. To save some time, one
employee suggested that they just weigh the first 30 trucks that come through the
station that day and treat that as representative of all trucks. Why isn’t this method a
good idea?
(c) Another official suggests that they just weigh every twentieth truck that passes
through the station that day. Explain why this method is NOT an SRS.