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. (a) state the null hypothesis in words. choose the correct answer below. a. the standard deviation in the pressure required to open any valve is 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 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.

Explanation:

The null hypothesis is a statement of no change. In this context, since the original standard deviation is known to be 1.3 psi and we are testing if variability (standard deviation) has increased, the null hypothesis in words should be that the standard deviation remains at 1.3 psi for the specific valve in question. Option A says "any valve" which is incorrect as the problem is about "a certain valve". Option C is the null hypothesis as it represents the status - quo (no increase in standard deviation). Option D is about difference (not just increase) and Option B is a mis - statement (the original is known to be 1.3, we are testing a change).

Answer:

C. The standard deviation in the pressure required to open a certain valve is 1.3 psi.