A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 22 bottles and finds the average amount of liquid held by the bottles is $9.7$ ounces with a standard deviation of $.2$ ounce. Which of the following is the set of hypotheses the company wishes to test? A) $H _ { 0 } : \mu 10$ C) $H _ { 0 } : \mu = 10$ vs. $H _ { \mathrm { a } } : \mu \neq 10$ D) $H _ { 0 } : \mu = 10$ vs. $H _ { \mathrm { a } } : \mu

Question

A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 22 bottles and finds the average amount of liquid held by the bottles is $9.7$ ounces with a standard deviation of $.2$ ounce. Which of the following is the set of hypotheses the company wishes to test?
A) $H _ { 0 } : \mu < 10$ vs. $H _ { \mathrm { a } } : \mu = 10$
B) $H _ { 0 } : \mu = 10$ vs. $H _ { \mathrm { a } } : \mu > 10$
C) $H _ { 0 } : \mu = 10$ vs. $H _ { \mathrm { a } } : \mu \neq 10$
D) $H _ { 0 } : \mu = 10$ vs. $H _ { \mathrm { a } } : \mu < 10$

Quizplus · Accepted Answer

The null hypothesis ($H_0$) is typically a statement of no effect or no difference, which in this case is that the bottles hold the claimed amount of 10 ounces ($\mu = 10$). The alternative hypothesis ($H_a$) is what the company is testing against the null, which based on the complaints, is that the bottles hold less than the claimed amount ($\mu < 10$).

A Bottling Company Produces Bottles That Hold 10 Ounces of Liquid