Homework 2 - Statistics

Homework 2
Due in class, Feb. 3rd
Instructions: Two problems are included in the first homework. No need
to use R.
Problem 1 Airfreight breakage
Refer to the Airfreight Breakage data in homework 1
i: 1 2 3 4 5 6 7 8 9 10
Xi: 1 0 2 0 3 1 0 1 2 0
Yi: 16 9 17 12 22 13 8 15 19 11
a. Set up the ANOVA table. (calculate the SSE, SSR, SSTO, d.f., MSE
and MSR)
b. Conduct an F test to determine whether or not there is a linear association
between the number of times a carton is transferred and the
number of broken ampules; control α risk at 0.05. State the hypotheses,
the test-statistic, the decision rule and the conclusion.
c. Calculate R 2 and r. What proportion of the variation in Y is accounted
for by introducing X into the regression model?
Problem 2 Property Assessments
The data that follow show assessed value for property tax purposes (Y1, in
thousand dollars) and sales price (Y2, in thousand dollars)for a sample of
15 parcels of land for industrial development sold recently in ”arm’s length”
transactions in a tax district.
i: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Yi1: 13.9 16.0 10.3 11.8 16.7 12.5 10.0 11.4 13.9 12.2 15.4 14.8 14.9 12.9 15.8
Yi2: 28.6 34.7 21.0 25.5 36.8 24.0 19.1 22.5 28.3 25.0 31.1 29.6 35.1 30.0 36.2
a. Obtain the Spearman rank correlation coefficient rs
1

. Test by means of the Spearman rank correlation coefficient whether an
association exists between property assessments and sales prices using
test statistic t ∗ with α = 0.01. State the hypotheses, the test-statistic,
the decision rule and the conclusion.
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