The housing commission of Woodcreek County is interested in finding more about t
ID: 2985081 • Letter: T
Question
The housing commission of Woodcreek County is interested in
finding more about the number of rental units that do not
meet
standard living requirements in both Ridge Township and
Crystal
Township. Units are randomly selected in both cities. Of the
85
units sampled in Ridge Township(call this Township 1), 17 do
not
meet the requirements. Of the 80 units sampled in Crystal
Township(call this Township 2), 24 do not meet the
requirements.
a. What is the estimate for the proportion of rental units
that
do not meet the requirements in Township 1?
b. What is the estimate for the proportion of
rental
units that do not meet the requirements in Township 2?
c. What are the hypotheses to test in the proportions of
rental
units that do not meet the requirements in the two townships
are
equal or not?
d. What is the value of the z statistic for testing for
equality
of the proportions of rental units that do not meet the
requirements in the two townships?
e. At the 10% significance level, is the observed difference
in
sample proportions statistically significant? Explain
briefly.
Explanation / Answer
a) estimate for the proportion of rental units that do not meet the requirements in
Township 1, P1 = 17/85 = 1/5 = 0.2
b) estimate for the proportion of rental units that do not meet the requirements in
Township 2, P2 = 24/80 = 0.3
c) hypotheses to test in the proportions of rental units that do not meet the
requirements in the two townships are equal or not
H0: p1 = p2
HA : p1 not equal to p2
d) (Z = rac{(p1-p2)-0}{sigma1/sqrt{n1} + sigma2/sqrt{n2} })
e) Zcritical = (0.3-0.2)/ (0.043 + 0.051) = 0.1/ 0.094 = 1.063
Z (0.10) = 1.645
Zcritical < Z (0.10)
Yes, At the 10% significance level, is the observed difference in sample proportions
statistically significant
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