Manual Transmission Automobiles In a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130 cars, 30 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 95% confidence. Round intermediate and final answers to at least three decimal places.
Manual Transmission Automobiles In a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130 cars, 30 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 95% confidence. Round intermediate and final answers to at least three decimal places.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Manual Transmission Automobiles In a recent year, 6% of cars sold had a
manual transmission. A random sample of college students who owned cars
revealed the following: out of 130 cars, 30 had manual transmissions.
Estimate the proportion of college students who drive cars with manual
transmissions with 95% confidence. Round intermediate and final answers to
at least three decimal places.
<p<
Transcribed Image Text:Sample Question
Manual Transmission Automobiles In a
recent year, 6% of cars sold had a manual
transmission. A random sample of college
students who owned cars revealed the
following: out of 128 cars, 30 had manual
transmissions. Estimate the proportion of
college students who drive cars with manual
transmissions with 99% confidence. Round
intermediate and final answers to at least three
decimal places.
Explanation
Formula for a Specific Confidence
Interval for a Proportion
2012 √2²
pq
pq
<p<p+za/2\
n
n
when np and nq are each greater
than or equal to 5.
Since a 1-0.99-0.01, Za/2=2.58.
Find and .
X 30
n
= 0.234
q=1-p=1-0.234
= 0.766
Calculate the confidence interval.
M
pq
pq
-²a/2
n
n
(0.234) (0.766)
(0.234) (0.766)
0.234-2.58
<p<0.234+2.58
128
128
0.234-0.097<p<0.234+0.097
0.137<p<0.331
Hence, we can be 99% confident that the
proportion of college students who drive stick
shift cars is between 13.7% and 33.1%, based on
a sample of 128 students.
128
<p<p+za/2\
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