Question

the standard deviation in the pressure required to open a certain valve is known to be $sigma = 1.3$ psi. due to changes in the manufacturing process, the quality - control manager feels that the pressure variability has increased
(a) state the null and alternative hypotheses in words.
(b) state the null and alternative hypotheses symbolically.
(c) explain what it would mean to make a type i error.
(d) explain what it would mean to make a type ii error.

b. the standard deviation in the pressure required to open a certain valve is 1.3 psi.
c. the standard deviation in the pressure required to open a certain valve is greater than 1.3 psi.
d. the standard deviation in the pressure required to open a certain valve is different from 1.3 psi.
state the alternative hypothesis in words. choose the correct answer below
a. the standard deviation in the pressure required to open a certain valve is different from 1.3 psi
b. the standard deviation in the pressure required to open a certain valve is 1.3 psi.
c. the standard deviation in the pressure required to open any valve is 1.3 psi.
d. the standard deviation in the pressure required to open a certain valve is greater than 1.3 psi.
(b) state the hypotheses symbolically
$h_0$: psi
$h_1$: psi
(type integers or decimals. do not round.)

Explanation:

• Null Hypothesis (\(H_0\)): It is a statement of no change or no difference. In the context of standard - deviation, it assumes that the standard deviation of the pressure required to open the valve is equal to the known value.
• Alternative Hypothesis (\(H_1\)): It is a statement that contradicts the null hypothesis. Since the quality - control manager feels the pressure variability (standard deviation) has increased, the alternative hypothesis will be that the standard deviation is greater than the known value.

Answer:

• \(H_0:\sigma = 1.3\) psi
• \(H_1:\sigma> 1.3\) psi