The standard deviation in the pressure required to open a certain valve is known to be σ=1.1 psi. Due to changes in the manufacturing​ process, the​ quality-control manager feels that the pressure variability has been reduced. ​(a) Determine the null and alternative hypotheses. ​(b) Explain what it would mean to make a Type I error. ​(c) Explain what it would mean to make a Type II error. ​(a) State the hypotheses.

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The standard deviation in the pressure required to open a certain valve is known to be
σ=1.1
psi. Due to changes in the manufacturing​ process, the​ quality-control manager feels that the pressure variability has
been reduced.
​(a)
Determine the null and alternative hypotheses.
​(b)
Explain what it would mean to make a Type I error.
​(c)
Explain what it would mean to make a Type II error.
​(a) State the hypotheses.
 
H0​:
sigmaσ
pp
sigmaσ
muμ
equals=
less than<
greater than>
equals=
not equals≠
1.11.1
H1​:
sigmaσ
muμ
sigmaσ
pp
greater than>
equals=
not equals≠
greater than>
less than<
1.11.1
​(Type integers or decimals. Do not​ round.)
​(b) Which of the following is a Type I​ error?
 
A.
The manager rejects the hypothesis that the pressure variability is
1.1​,
when it is the true pressure variability.
 
B.
The manager rejects the hypothesis that the pressure variability is
1.1​,
when the true pressure variability is
less
than
1.1.
 
C.
The manager fails to reject the hypothesis that the pressure variability is
1.1​,
when it is the true pressure variability.
 
D.
The manager fails to reject the hypothesis that the pressure variability is
1.1​,
when the true pressure variability is
less
than
1.1.
​(c) Which of the following is a Type II​ error?
 
A.
The manager rejects the hypothesis that the pressure variability is
1.1​,
when the true pressure variability is
less
than
1.1.
 
B.
The manager fails to reject the hypothesis that the pressure variability is
1.1​,
when it is the true pressure variability.
 
C.
The manager rejects the hypothesis that the pressure variability is
1.1​,
when it is the true pressure variability.
 
D.
The manager fails to reject the hypothesis that the pressure variability is
1.1​,
when the true pressure variability is
less
than
1.1.
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