An industrial concern has experimented with several different mixtures of the fo
ID: 3305189 • Letter: A
Question
An industrial concern has experimented with several different mixtures of the four components – magnesium, sodium nitrate, strontium nitrate, and a binder – that comprise a rocket propellant. The company has found that two mixtures in particular give higher flare-illumination values than the others. Mixture 1 consists of a blend composed of the proportions 0.4, 0.1, 0.42, and 0.08, respectively, for the four components of the mixture; mixture 2 consists of a blend using the proportions 0.6, 0.27, 0.1, and 0.05. Twenty different blends (10 of each mixture)are prepared and tested to obtain the flare-illumination values. These data appear here (in units of 1,000 candles).
Mixture 1 185 192 201 215 170 190 175 172 198 202 Mixture 2 221 210 215 202 204 196 225 230 214 217 a. Plot the sample data. Which test(s) could be used to compare the mean illumination values for the two mixtures? b. Give the level of significance of the test and interpret your findings.Explanation / Answer
a)
Here, we would be using two sample t-test with pooled variance assuming population variances to be equal.
b)
Level of significance=0.05
H0: 1 - 2 = 0 i.e. (1 = 2)
H1: 1 - 2 0 i.e. (1 2)
Assuming population variances are equal, we would have to calculate pooled-variance t-Test
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (10-1)*14.65^2+(10-1)*10.627^2/9+9
= 1932+1016.4/18
=163.8
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(190-213.4)-0/163.8(1/10+1/10)
=-23.4/5.7236
=-4.088
tCRIT is +-2.1 and hence reject the null hypothesis because tSTAT<tCRIT
Mixture 1 Mixture 2 185 221 192 210 201 215 215 202 170 204 190 196 175 225 172 230 198 214 202 217 190 213.4 Mean 14.65150732 10.62700961 Std Dev