An engineer conducted an experiment to compare two metals: iron and co

Question

An engineer conducted an experiment to compare two metals: iron and copper, as bonding agents for an alloy material. Components of the alloy were bonded using the metals as bonding agents, and the pressures required to break the bonds were measured. The data for the breaking pressures are given in the following table:

S. No	Breaking Pressure
S. No	Iron	Copper
1	72.7	73
2	69.6	67.2
3	83.4	75.3
4	78.9	61.4
5	75	74
6	71.6	69.5
7	85.7	69.8
8	73.5	73.8
9	70.4	68
10	84.2	76.1

If the breaking pressures for both iron and copper are normally distributed, are the variances of the distributions of the breaking pressure of iron and copper equal at 5 % level of significance?

19 Apr 2025

Answer :

Word Count : 638

We are asked to test whether the variances of breaking pressures for iron and copper are equal at a 5% significance level. This is an F-test for equality of variances. Let’s solve step by step manually. Step 1: Collect data Iron: 72.7, 69.6, 83.4, 78.9, 75, 71.6, 85.7, 73.5, 70.4, 84.2 Copper: 73, 67.2, 75.3, 61.4, 74, 69.5, 69.8, 73.8, 68, 76.1 Step 2: Compute means Mean of iron ($\bar{X}_1$): $$ \bar{X}_1 = \frac{72.7+69.6+83.4+78.9+75+71.6+85.7+73.5+70.4+84.2}{10} $$ Step by step addition: * 72.7 + 69.6 = 142.3 * 142.3 + 83.4 = 225.7 * 225.7 + 78.9 = 304.6 * 304.6 + 75 = 379.6 * 379.6 + 71.6 = 451.2 * 451.2 + 85.7 = 536.9 * 536.9 + 73.5 = 610.4 * 610.4 + 70.4 = 680.8 ________ _________ __________ __________ _____ ____ _____ _____ ________ ____ ______ _______.
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S. No.	Test For	Name of the Test	Test Statistic
1	Population mean when population variance is known and population is normal	Z-test	$Z=\frac{\bar{X}-\mu}{\sigma/\sqrt{n}}$
2	Population mean when population variance is unknown and population is normal
3	Difference of two population means when samples are paired, and population of differences follows normal distribution.
4	Difference of two population means when samples are independent, and population of differences follows normal distribution.
5	Population variance when the population is normal distributed
6	Population variance when the population is not normal distributed

Child	Age (in years
Sonu	2
Lavnik	4
Chiya	3
Amam	3
Avishi	4
Ridhi	5
Sidhi	3