Answer
a. $H_{o}: σ = 0.7 psi$
$H_{1}: σ < 0.7 psi$
b. Type-I Error: Sample evidence leads quality-control
manager to believe that the pressure variability has been reduced, however, in fact the pressure variability has not reduced.
c. Type-II Error: Sample evidence leads quality-control
manager to believe that the pressure variability has not been reduced, however, in fact the pressure variability has reduced.
Work Step by Step
a. Null hypothesis (the pressure variability is at 0.7 psi):
$H_{o}: σ = 0.7 psi$
Alternative hypothesis (the pressure variability is less than 0.7 psi):
$H_{1}: σ < 0.7 psi$
b. Type-I Error: Sample evidence leads quality-control
manager to believe that the pressure variability has been reduced, however, in fact the pressure variability has not reduced. In other words, the scientists have rejected the null hypothesis ($H_o$), but it in fact is true.
c. Type-II Error: Sample evidence leads quality-control
manager to believe that the pressure variability has not been reduced, however, in fact the pressure variability has reduced. In other words, the scientists have not rejected the null hypothesis ($H_o$), when in fact the alternative hypothesis ($H_1$) is true.
