(i) Construct a 95% confidence interval estimate for the population mean breaking tension based on the sample mean assuming an unchanged standard deviation. (ii) The manager of the elastic bands manufacturer claims that there is change in the mean breaking tension. Justify whether his claim is acceptable or not.
(i) Construct a 95% confidence interval estimate for the population mean breaking tension based on the sample mean assuming an unchanged standard deviation. (ii) The manager of the elastic bands manufacturer claims that there is change in the mean breaking tension. Justify whether his claim is acceptable or not.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Q3
(a)
A machine produces elastic bands with breaking tension normally distributed
with mean 45 N and standard deviation 4.36 N. In order to test whether there is a
change in the mean breaking tension, a random sample of 50 was tested and
found to have a mean breaking tension of 43.46 N.
(i)
Construct a 95% confidence interval estimate for the population mean
breaking tension based on the sample mean assuming an unchanged
standard deviation.
(ii)
The manager of the elastic bands manufacturer claims that there is change
in the mean breaking tension.
Justify whether his claim is acceptable or not.
(b)
The measurements of the heat-producing capacity (in millions of calories per ton)
of coal specimens from two mines is shown in Table Q3. Assume that the
populations are normally distributed, with the variances of population are
unknown but equal.
Table Q3: The heat-producing capacity of coal specimens
Mine 1
Mine 2
8400
7510
8230
7690
8380
7720
7860
8070
7930
7660
Calculate the test statistics whether the difference between the means of these two
samples is significant or not by using a level of significant of 0.05.
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