Question

The standard deviation in the pressure required to open a certain valve is known to be sigma equals 0.6 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.

Answer 1

( a ) The null hypothesis, represented by $H_{0}$, 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 -

$H_0: stigma = 0.7,\\H_a: stigma < 0.7$

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.