7.
Suppose
a
market
analyst
wants
to
determine
the
difference
in
the
average
price
if
a
gallon
of
whole
milk
in
Seattle
and
Atlanta.
To
do
so,
he
takes
a
telephone
survey
of
some
randomly
selected
consumers
in
Seattle.
He
then
takes
another
sample
of
some
respondents
from
Atlanta.
Use
the
following
sample
of
prices
of
a
gallon
of
milk
in
both
the
cities,
solve
the
following
questions.
Sample 1
Seattle
$2.55 $2.36
2.67
2.54
2.50
2.54
2.61
2.80
3.10
2.61
(i) Test
the
hypothesis
that
H0: σ 1
2
Sample 2
Atlanta
$2.23 $2.40
2.30
2.33
2.19
2.29
2.41
2.18
$2.43
2.43
2.38
2.49
2.57
$2.39
2.40
2.23
2.29
2
2
2
= σ 2
against
the
alternative
hypothesis
H0: σ 1 ≠ σ 2
at
5%
label
of
significance.
(a) What is the point estimate of the difference between the two population mean difference
µ Seattle − µ Atlanta ?
(b) Test the hypothesis that
H 0 : µ Seattle − µ Atlanta = 0
against
H a : µ Seattle − µ Atlanta ≠ 0 .
Use 5% level of significance. Show all six steps. Use Classical approach and p-value approach.
8. The following information was obtained from matched samples.
The daily production rates for a sample of workers before and after a training program are shown below.
Worker
Before
After
1
20
22
2
25
23
3
27
27
4
23
20
5
22
25
6
20
19
7
17
18
Questions:
(i)
Estimate
the
point
estimate
for
the
difference
between
the
means
of
the
two
populations
µ d = µ A − µ B .
≤ 0
against
H a : µ d >
0
at
5%
label
of
significance,
(ii)
Test
the
null
hypothesis
H0:
µ d
(iii)
Compute
a
95%
confidence
interval
for
the
difference
between
the
means
of
the
two
populations
µ d = µ A − µ B .
