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(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
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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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.
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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