The housing commission of Woodcreek County is interested in finding more about t
ID: 2985046 • 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) 17/85= 0.2
b) 24/80= 0.3
c) Ho: p1=p2
Ha: p1=/p2
d) z= (0.3-0.2)/sqrt(.3*.7/80 +.2*.8/85) = 1.49
e) Critical value from z table at .1 level is 1.645.
Since 1.49 is less than 1.645 this is not statistically significant and there is insufficient evidence to reject H0 and say there is a difference between the proportions.
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