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Lab 3:
The Sampling Distribution, Interval Estimation, Correlation and Covariance
Objectives:
1.
Still more practice with Excel: equations and functions.
2.
Bivariate distributions
– relationship between two variables.
3.
Introduce the concepts of
covariance
and
correlation
– variables that are related to each other.
4.
Descriptive measures
of covariance and correlation.
Key Terms:
1.
Scatter Diagrams
/ XY Graphs.
2.
Covariance
and
correlation
.
Data
:
Your Excel file from Lab 2, which continues our use of the Excel file: AmherstHomeSales2006
.xlsx
.
And an additional data set on home prices in Belchertown and Amherst.
Exercises:
♦
TwoSample Hypothesis Test of Means
1.
The question we ask is: ‘Are the population mean house prices the same in Amherst and
Belchertown?’
Thus, our hypothesis can be stated: H
0
:
μ
A
=
μ
B
;
H
A
:
μ
A
≠
μ
B
.
2.
If the sample means for both Amherst and Belchertown homes are normally distributed (CLT
here), then the difference is also normal, and we an apply the Ztest, or ttest if we don’t know the
true standard deviations.
3.
We presume no knowledge of the true population standard deviations. Thus, our safest choice for
test statistics is a formulation that assumes unequal variances:
()
12
22
calc
XX
t
ss
nn
μ
−−
−
=
⎛⎞
+
⎜⎟
⎝⎠
, the degrees of freedom calculation for this statistic is a bit
involved and will fall somewhere between the sample sizes for the two samples. Luckily, as we’ll
see, Excel takes care of this for us.
4.
We could easily calculate that in Excel, but if we go to
Data
and
Data Analysis
, we’ll find
ttest:
TwoSample Assuming Unequal Variances
.
Click OK. The next window asks for the data range
for each of the “two variables.” Here, we’ll treat the Amherst prices and Belchertown prices as
different variables. Whoa!
What do we need to do first before trying this test??
5.
Right, once you’ve done that, highlight the Amherst prices for Variable 1 and the Belchertown
prices for Variable 2.
What is the
Hypothesized Mean Difference
? You also get to choose
α
. Then
select the
Output Range
: a cell with lots of space below and to the right. Now click OK and
Bingo!
Your twosample ttest is complete.
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This note was uploaded on 12/08/2011 for the course ECON 312 taught by Professor Daniellass during the Winter '10 term at UMass (Amherst).
 Winter '10
 DanielLass

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