ISOM 111 L7L8, Fall 2010
1
Homework 5
Due: Friday, Nov 26, 4:00pm
Submit to the “ISOM 111 L7L8 Homework Collection Box” outside Room 4351
I
. In a news story distributed by the
Washington Post
, Lew Sichelman reports that a substantial
fraction of mortgage loans that go into default within the first year of the mortgage were approved on
the basis of falsified applications. For instance, loan applicants often exaggerate their income or fail
to declare debts. Suppose that a random sample of 1,000 mortgage loans that were defaulted within
the first year reveals that 410 of these loans were approved on the basis of falsified applications.
(a). Find a point estimate of and a 95 percent confidence interval for
p
, the proportion of all
firstyear defaults that are approved on the basis of falsified applications.
(b). Based on your interval, what is a reasonable estimate of the minimum percentage of firstyear
defaults that are approved on the basis of falsified applications?
(c). Based on your 95% confidence interval found in part (a), find the sample size needed so that
the margin of error at 95% confidence will be no more than 2%.
II
. Recall from Exercise II of Homework 4 that Bayus (1991) studied the mean numbers of auto
dealers visited by early and late replacement buyers.
(a). Letting
μ
be the mean number of dealers visited by early replacement buyers, suppose that
we wish to test
H
0
:
μ
≥
4
versus
H
a
:
μ <
4
.
A random sample of 800 early replacement
buyers yields a mean number of dealers visited of
¯
x
= 3
.
3
. Assuming
σ
equals .71, calculate
the
p

value and test
H
0
versus
H
a
at
α
= 0
.
01
significance level. Interpret your result.
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 Spring '11
 Hong
 Null hypothesis, ISOM, mean performance rating

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