1. Suppose the local Childhood lead Poisoning Prevention Council in a metropolitan area in a western United State undertakes the responsibility of determining the proportion of homes in a certain development of 120 homes with unsafe lead levels. Because of the great expense involved in performing spectrometric testing of interior walls, ceilings, floors, baseboards, cabinets, and other obvious lead hazards such as crib bars, as well as of exterior sidings, porches and porch rails, it was decided to select a sample of homes for a study. A good up-to-date frame exists for sampling purposes. This frame is a street listing containing the address and owner of each home for each of the streets in the target area. It was decided to select a one-in-three (1-in- 3) sample of homes. Let us assume that the only houses with serious lead hazard problems are the 26th, 27th, 28th, and 29th on the list. a. Suppose the random number 2 was chosen to start the sequence. Estimate the proportion of homes with lead hazards from the sample. b. Obtain a 95% confidence interval for the proportion of homes with lead hazards. What assumptions did you make? C. What is the true variance of the distribution of the estimated proportion of homes with lead hazards? How does this compare with the variance estimated in part (b)? d. Suppose that a simple random sample of 40 homes had been selected instead. What is the variance of the distribution of the estimated proportion of lead hazardous homes in this case? How does this value compare with the variance from a 1-in-3 systematic sample?
1. Suppose the local Childhood lead Poisoning Prevention Council in a metropolitan area in a western United State undertakes the responsibility of determining the proportion of homes in a certain development of 120 homes with unsafe lead levels. Because of the great expense involved in performing spectrometric testing of interior walls, ceilings, floors, baseboards, cabinets, and other obvious lead hazards such as crib bars, as well as of exterior sidings, porches and porch rails, it was decided to select a sample of homes for a study. A good up-to-date frame exists for sampling purposes. This frame is a street listing containing the address and owner of each home for each of the streets in the target area. It was decided to select a one-in-three (1-in- 3) sample of homes. Let us assume that the only houses with serious lead hazard problems are the 26th, 27th, 28th, and 29th on the list. a. Suppose the random number 2 was chosen to start the sequence. Estimate the proportion of homes with lead hazards from the sample. b. Obtain a 95% confidence interval for the proportion of homes with lead hazards. What assumptions did you make? C. What is the true variance of the distribution of the estimated proportion of homes with lead hazards? How does this compare with the variance estimated in part (b)? d. Suppose that a simple random sample of 40 homes had been selected instead. What is the variance of the distribution of the estimated proportion of lead hazardous homes in this case? How does this value compare with the variance from a 1-in-3 systematic sample?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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Transcribed Image Text:1. Suppose the local Childhood lead Poisoning Prevention Council in a metropolitan
area in a western United State undertakes the responsibility of determining the
proportion of homes in a certain development of 120 homes with unsafe lead levels.
Because of the great expense involved in performing spectrometric testing of interior
walls, ceilings, floors, baseboards, cabinets, and other obvious lead hazards such as
crib bars, as well as of exterior sidings, porches and porch rails, it was decided to
select a sample of homes for a study. A good up-to-date frame exists for sampling
purposes. This frame is a street listing containing the address and owner of each home
for each of the streets in the target area. It was decided to select a one-in-three (1-in-
3) sample of homes. Let us assume that the only houses with serious lead hazard
problems are the 26th, 27th, 28th, and 29th on the list.
a. Suppose the random number 2 was chosen to start the sequence. Estimate the
proportion of homes with lead hazards from the sample.
b. Obtain a 95% confidence interval for the proportion of homes with lead
hazards. What assumptions did you make?
C. What is the true variance of the distribution of the estimated proportion of
homes with lead hazards? How does this compare with the variance estimated
in part (b)?
d. Suppose that a simple random sample of 40 homes had been selected instead.
What is the variance of the distribution of the estimated proportion of lead
hazardous homes in this case? How does this value compare with the variance
from a 1-in-3 systematic sample?
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