months (January to June) observations are recorded for 124 trading
days. For the period July to December observations are available for
128 trading days.
An exercise of interest is to find a 95% confidence interval estimate
for the difference between the population mean closing price in the
two sample periods.
Stock market prices adjust rapidly to the arrival of new information.
Therefore, it is reasonable to consider that the two samples are
independent.
Summary statistics for the closing prices for the two sample periods
are:
January to June
124
=
x
n
89.96
$
x
=
32.54
=
2
x
s
July to December
128
=
y
n
97.98
$
y
=
21.45
=
2
y
s
The pooled variance estimate is:
26.91
=
2
s
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View Full DocumentEcon 325 – Chapter 8
11
A confidence interval estimate is calculated as:
128
26.91
124
26.91
97.98
89.96
+
±

c
t
)
(
A tdistribution critical value
c
t
for a 95% interval estimate is
needed. The degrees of freedom is:
250
2
128
124
=

+
=

+
)
2
n
n
(
y
x
The Appendix Table for the tdistribution does not have an entry for
250 degrees of freedom.
However, for
0.025
2
0.05
=
=
α
2
,
0.025
1.96
1.96
=
>
≅
>
)
Z
(
P
)
t
(
P
)
250
(
where
Z
is the standard normal random variable.
With Microsoft Excel the Function
TINV(0.05, 250) returns the
answer:
1.969
=
c
t
.
Econ 325 – Chapter 8
12
Calculations give a 95% interval estimate for the difference in means
for the closing prices in the two sample periods as:
[
6.73
9.31


,
]
A 99%
interval estimate is wider.
With
0.01
=
α
the Microsoft Excel Function
TINV(0.01, 250)
gives
the critical value:
2.596
=
c
t
.
For a 99% interval estimate the lower and upper limits are:
[
6.32
9.72


,
]
The value zero is outside the range of the calculated interval estimate
to suggest that the mean closing price is lower in the first sample
period compared to the second sample period.
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 Fall '10
 WHISTLER
 Normal Distribution, Variance, confidence interval estimate, interval estimate

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