To: sbaker@odu.edu
From: Thomas Meyer
tmeyer@ph.vccs.edu
276 656-0283
Patrick Henry Community College
Subject: Statistics - w/ Dr.Spencer Baker - Homework Assignment #3, Ch 9 - Problem 14, page242.
Date: March 20, 2004
General Algortithm:
Use the methodology on page 235-236
(From 4000 seniors, ten per cent are to be sampled, that is 400.
Reason that 10% of the sample of 400 should be in Arts, that is, 40;
Reason that 15% of the sample should be in Social Sciences, that is, 60, and so
forth.)
Question:
For each of the following, determine the number of participants needed for each
cell of a stratified random sample.
a. Suppose that a high school district within a
metropolitan area has 20,000 graduating seniors. They want to survey 5% of
these students one year after graduating about the quality of their educational
experience. They have decided to survey students based on the following
criteria:
attended a four-year college or university (20%);
attended a two-year community college (15%):
attended a technical/vocational school (40%);
or worked or enlisted in the military (25%).
Answer:
Five % of 20,000 is 1000 students.
Reason that 20% who attended a 4-year or university are 20% of 1000 or
200.
Reason that 15% who attended a 2-year are 15% of 1000 or
150.
Reason that 40% who attended technical/vocational school are 40% of 1000 =
400.
Reason that 25% who worked or enlisted in the military are 25% of 1000 =
250.
Then 200 + 150 + 400 + 250 = 1000 and represent the desired percentages and total students to be surveyed.
Question:
b. Suppose a researcher is interested in determining if there
is a gender (female vs. male) and age category [adolescents (age 12-18) vs.
young adults (age 19-25)] difference in the United States on a measure of
responsibility. Assume that the proportion of males and females and the
proportion of adolescents and young adults is the same in the United States.
Find the number of participants in each category if the researcher wants a
sample size of 1,500.
Answer:
You need 750 males and 750 females.
Among the
men you need 325 aged 12-18 and 325 aged 19-25.
Among the women you need 325 aged 12-18 and 325 aged 19-25.
Question:
c. A social psychologist is interested in conducting a survey
of people who are of legal voting age in the United States. However, the
researcher wants a gender breakdown (female vs. male) and an education breakdown
(no high school diploma, high school diploma only, some post-secondary education
credits, college/university degree) to be reflected in the final sample.
Suppose the gender breakdown for this group based on the latest available data
is 52% female and 48% male. In addition, suppose the educational breakdown
is such that 10% do not have a high school diploma, 25% have a high school
diploma only, 35% have some post-secondary education credits, and 30% have a
college/university degree. Suppose the desired sample size is 1,000.
Given only the information above, how many participants should be in each group?
Answer:
Separate the desired sample size of 1000 into males and
females using the 52% female and 48% male ratio given.
Therefore 520 will be female and 480 will be male.
Then multiply the number in each sex by the educational attainment percentages.
For women:
520 X 10% with no high school diploma is 52 women;
520 X 25% with a high school diploma is 130 women;
520 X 35% with some post-secondary education credits is 182 women;
520 X 30% with a college/university degree is 156 women.
This adds to 52 + 130 + 182 + 156 = 520 women.
For men:
480 X 10% with no high school diploma is 48 men;
480 X 25% with a high school diploma is 120 men;
480 X 35% with some post-secondary education credits is 168 men;
480 X 30% with a college/university degree is 144 men.
This adds to 48 + 120 + 168 + 144 = 480 men.
filename: StatHW3Ch9Prob14page242TomMeyer.doc
Tom Meyer
Thomas Meyer