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A melting point test of n = 10 samples of a binder used in
Chapter 9, Problem 44E(choose chapter or problem)
A melting point test of n = 10 samples of a binder used in manufacturing a rocket propellant resulted in \(\bar x = 154.2^\circ~\mathrm F\) Assume that the melting point is normally distributed with \(\sigma =1.5 ^\circ~\mathrm F\)
(a) Test \(H_0: \mu = 155\) versus \(H_1: \mu \neq 155\) using \(\alpha = 0.01\).
(b) What is the P-value for this test?
(c) What is the \(\beta\)-error if the true mean is \(\mu = 150\)?
(d) What value of n would be required if we want \(\beta < 0.1\) when \(\mu = 150\)? Assume that \(\alpha = 0.01\).
Questions & Answers
QUESTION:
A melting point test of n = 10 samples of a binder used in manufacturing a rocket propellant resulted in \(\bar x = 154.2^\circ~\mathrm F\) Assume that the melting point is normally distributed with \(\sigma =1.5 ^\circ~\mathrm F\)
(a) Test \(H_0: \mu = 155\) versus \(H_1: \mu \neq 155\) using \(\alpha = 0.01\).
(b) What is the P-value for this test?
(c) What is the \(\beta\)-error if the true mean is \(\mu = 150\)?
(d) What value of n would be required if we want \(\beta < 0.1\) when \(\mu = 150\)? Assume that \(\alpha = 0.01\).
ANSWER:Step 1 of 7
Given,
Sample size, n = 10
The sample mean,
The standard deviation,
Using the given values let’s determine the following: