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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