Economics 403A: Homework 3
Fall 2018, UCLA
Instructor: Dr. Rojas
Due Date: Oct 18, 2018
All problems require detailed worked out solutions to receive full credit. All problems are worth
the same.
1. An article in The Engineer (\Redesign for Suspect Wiring," June 1990) reported the results of
an investigation into wiring errors on commercial transport aircraft that may produce faulty
information to the ight crew. Such a wiring error may have been responsible for the crash
of a British Midland Airways aircraft in January 1989 by causing the pilot to shut down the
wrong engine. Of 1600 randomly selected aircraft, eight were found to have wiring errors that
could display incorrect information to the ight crew.
(a) Find a 99% con dence interval on the proportion of aircraft that have such wiring errors.
(b) Suppose we use the information in this example to provide a preliminary estimate of
p. How large a sample would be required to produce an estimate of p that we are 99%
con dent di ers from the true value by at most 0.008?
(c) Suppose we did not have a preliminary estimate of p. How large a sample would be
required if we wanted to be at least 99% con dent that the sample proportion di ers
from the true proportion by at most 0.008 regardless of the true value of p?
(d) Comment on the usefulness of preliminary information in computing the needed sample
size.
2. The proportion of residents in Phoenix favoring the building of toll roads to complete the
freeway system is believed to be p= 0:3. If a random sample of 10 residents shows that 1 or
fewer favor this proposal, we will conclude that p 0, for the purpose of
testing
H0 ∶ = 1
H1 ∶ > 1
The null hypothesis will be rejected if y≥ 3:20.
(a) Calculate the probability of committing a Type I error.
(b) Calculate the probability of committing a Type II error when = 4slash.left3.
(c) Draw a diagram that shows the and calculated in parts (a) and (b).
7. Evans Rosenthal: 5.4.12
{ 3 {
8. Evans Rosenthal: 5.5.18
9. Evans Rosenthal: 6.2.17
10. Evans Rosenthal: 6.2.25
11. Evans Rosenthal: 6.3.22
12. Evans Rosenthal: 6.4.17