Respuesta :
( a ) The null hypothesis, represented by [tex]H_{0}[/tex], should be equivalent to 0.6 pounds per square inch, considering it normally is predicted to be equivalent to the population parameter, which, in this case, is 0.6 psi ( pounds per square inch. ) The alternative hypothesis on the other hand contradicts the null hypothesis, and as the manager feels the pressure has been reduced, the alternative hypothesis points that the pressure is less than 0.6 psi -
[tex]H_0: stigma = 0.7,\\H_a: stigma < 0.7[/tex]
stigma is represented by the sign ( σ )
( b ) Now if you were to reject the null hypothesis when true, that would lead to a type I error. That would mean that to reject the fact that σ = 0.7, and accept that σ < 0.7, even though σ = 0.7 is true, would make a type I error.
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( c ) A type II error is quite the opposite. Accepting the null hypothesis while rejecting the alternative hypothesis would make a type II error.
From the information given and using error concepts, it is found that:
a)
The null hypothesis is [tex]H_0: \sigma = 0.6[/tex]
The alternative hypothesis is [tex]H_1: \sigma < 0.6[/tex]
b) It would mean a conclusion that the standard deviation is of less than 0.6 psi when in fact it is not.
c) It would mean a conclusion that the standard deviation not significantly less than 0.6 psi when in fact it is.
At the null hypothesis, we test if the standard deviation is of 0.6 psi, that is:
[tex]H_0: \sigma = 0.6[/tex]
At the alternative hypothesis, we test if variability has been reduced, that is, if the standard deviation is of less than 0.6 psi, hence:
[tex]H_1: \sigma < 0.6[/tex]
Item b:
A Type I error happens when a true null hypothesis is rejected, hence, it would mean a conclusion that the standard deviation is of less than 0.6 psi when in fact it is not.
Item c:
A Type II error happens when a false null hypothesis is not rejected, hence, it would mean a conclusion that the standard deviation not significantly less than 0.6 psi when in fact it is.
A similar problem is given at https://brainly.com/question/24296958
