Suppose that in a small private university with 4000 undergraduate students, 1600 students (40%) plan to go to graduate school. We are going to take a poll of 50 randomly selected students. We will look at the percentage of these randomly selected students who plan to go to graduate school. (a) Write down the box model. Be sure to include the values on the tickets, the
Suppose that in a small private university with 4000 undergraduate students, 1600 students (40%) plan to go to graduate school. We are going to take a poll of 50 randomly selected students. We will look at the percentage of these randomly selected students who plan to go to graduate school. (a) Write down the box model. Be sure to include the values on the tickets, the
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Transcribed Image Text:Suppose that in a small private university with 4000 undergraduate students, 1600
students (40%) plan to go to graduate school. We are going to take a poll of 50
randomly selected students. We will look at the percentage of these randomly
selected students who plan to go to graduate school.
(a) Write down the box model. Be sure to include the values on the tickets, the
number of repeats of each value, and the number of times we'll draw from the box
with replacement. (Remember, that we can use the box model where we draw with
replacement as a good approximation to randomly sampling from a population, as
long as the number of individuals sampled is small relative to the population.)
(b) The average of the ticket values in the box is
and the SD is
(c) The expected value of the percentage of the 50 sampled students who plan to
go to graduate school is
%, and the standard error is
%.
(d) A sample of size 50 seems small. Using the relevant rule of thumb discussed in
lecture, is it ok to use the normal approximation to find the chance that the
percentage of the 50 students who plan to go to graduate school is in a specific
interval, such as between 70% and
80%?
YES or NO (circle one) and justify your answer:
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