This preview shows pages 1–3. Sign up to view the full content.
Statistics 371 Assignment 5
Solution
1.
A provider of large digital switches is trying to assess future demand from its current
customers. The company selects 25 customers at random from its data base of 875
companies that have made a purchase in the past two years. They survey each
selected company by intensive interview to get a measure of the potential number of
switches that may be purchased in the next two years. The goal is to estimate the total
number of switches that may be purchased. From the data base, they know the
average number of switches purchased in the previous two years was () 1
4
.
7
x
μ
=
.
The data are available in the file ass5q1.txt .
a)
Prepare a scatterplot of
y
versus
x
We see from the plot that y tends to increase as x increases
b)
Estimate
()
y
using the sample average, the ratio estimate and the regression
estimate.
From R we have
. Note
that
is the least squares estimate of
±
.,
±
. ,
±
±
/
±
() . ,
±
.474
μμ
θ
β
yx
y
x
==
=
=
=
17 0
13 96
1218
1
±
from fitting the model
y
x
~
in R but that
±
is not the estimate of the slope produced by fitting the
model
y
x
~
−+
1
.
So we have the sample average is
±
.
y
=
17 0, the ratio estimate is
±
.
±
.
y
x
x
ratio
17 0
17 90 and the regression estimate is
±
( )
.
.474( ( )
±
)
.
x
reg
=+
−
=
17 0 1
18 09
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Documentc)
Find 95% confidence intervals for the total number of potential purchases based
on each estimate.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 AHMED
 Statistics

Click to edit the document details