Prof. Shihao Yang (shihao.yang@isye.gatech.edu)
1
2
ISyE 4031
Regression and Forecasting
HW #1
Problem 1
A melting point test of n = 10 samples of a binder used in manufacturing a rocket propellant
resulted in
࠵?̅
= 154.2
℉
. Assume that the melting point is normally distributed with
࠵?
=
1.5
℉
.
(a)
Test H
0
: μ = 155 versus H
1
: μ ≠ 155 using α = 0.01.
(b)
What is the P-value for this test?
(c)
What is probability of committing a type II error (i.e., β), if the true mean is μ = 150?
Problem 2
The brightness of a television picture tube can be evaluated by measuring the amount of current
required to achieve a particular brightness level. A sample of 10 tubes results in
࠵?̅
= 317.2
and s
= 15.7. Find (in microamps) a 99% confidence interval on mean current required. State any
necessary assumptions about the underlying distribution of the data.
Problem 3
Consider the hypothesis test
H
0
: μ
1
= μ
2
against
H
1
: μ
1
≠ μ
2
.
Suppose that sample sizes are
n
1
=
15
and
n
2
= 15,
that
࠵?̅
1
= 4.7
and
࠵?̅
2
= 7.8
, and that
࠵?
2
= 4
and
࠵?
2
= 6.25
. Assume that
σ
1
2
= σ
2
2
and
that the data are drawn from normal distributions. Use
α = 0.05
.
(a)
Test the hypothesis
(b)
Find the P-value.
Problem 4
Two chemical companies can supply a raw material. The concentration of a particular element in
this material is important. The mean concentration for both suppliers is the same, but you suspect
that the variability in concentration may differ for the two companies. The standard deviation of
concentration in a random sample of n
1
= 10 batches produced by company 1 is s
1
= 4.7 grams
per liter, and for company 2, a random sample of n
2
= 16 batches yields s
2
= 5.8 grams per liter.
Is there sufficient evidence to conclude that the two population variances differ? Use α = 0.05.
