A paper company has about 50 paper mills distributed over 3 provinces. The 50 papermills have a total of 600 machines. Lately it was found that some of the paper the company produces has a thickness above the specification of 2mm. From historical data it was found that the mean paper thickness 1.3mm the variance of 2. Answer the following questions. 1.1. A sample (without replacement) from 10 papermills across the two provinces was taken which have a total of 80 machines in the sample. From the sample it was determined that the average thickness of the paper produced by the machines was 1.2mm and the standard error of the thickness was 1.3 mm. Find the variance of the mean and the estimated standard error of the mean thickness of the paper of the sample. 1 1.2. Further investigation found that the proportion of machines that produces thickness over the limit in the 50 paper mills is 60%. If this proportion was to be estimated form the sample of machines from the 10 paper mills as p, find the standard error of this proportion.
A paper company has about 50 paper mills distributed over 3 provinces. The 50 papermills have a total of 600 machines. Lately it was found that some of the paper the company produces has a thickness above the specification of 2mm. From historical data it was found that the mean paper thickness 1.3mm the variance of 2. Answer the following questions. 1.1. A sample (without replacement) from 10 papermills across the two provinces was taken which have a total of 80 machines in the sample. From the sample it was determined that the average thickness of the paper produced by the machines was 1.2mm and the standard error of the thickness was 1.3 mm. Find the variance of the mean and the estimated standard error of the mean thickness of the paper of the sample. 1 1.2. Further investigation found that the proportion of machines that produces thickness over the limit in the 50 paper mills is 60%. If this proportion was to be estimated form the sample of machines from the 10 paper mills as p, find the standard error of this proportion.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
Related questions
Question
Transcribed Image Text:1.3. Find the estimated standard error of the proportion if, in the sample of machines, 36 machines had
produced paper that is thicker than the average. Is this a good estimate?
1.4. Find the estimated variance of the sample mean and its appropriate standard error. Explain your
answer.
1.5. Assume the number of machines in each of the papermills across only 2 provinces are known. The
number of faulty machines each paper mill is not known.
Stratum
Province 1
Province 2
N
200
300
W
0.4
1.4
1.5
0.6
1.05
1.4
Due to a constraint we can only take a sample of 100 machines form the total number of machines
over the 2 provinces.
1.5.1 Find the sample sizes to use.
1.5.2. Find the variance of the stratified mean based on the constraint that n, + nz = 100.
Transcribed Image Text:Question 1
A paper company has about 50 paper mills distributed over 3 provinces. The 50 papermills have a total
of 600 machines. Lately it was found that some of the paper the company produces has a thickness
above the specification of 2mm. From historical data it was found that the mean paper thickness 1.3mm
the variance of 2. Answer the following questions.
1.1. A sample (without replacement) from 10 papermills across the two provinces was taken which have
a total of 80 machines in the sample. From the sample it was determined that the average thickness
of the paper produced by the machines was 1.2mm and the standard error of the thickness was 1.3
mm. Find the variance of the mean and the estimated standard error of the mean thickness of the
paper of the sample.
1
1.2. Further investigation found that the proportion of machines that produces thickness over the limit in
the 50 paper mills is 60%. If this proportion was to be estimated form the sample of machines
from the 10 paper mills as p, find the standard error of this proportion.
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