A machine fills 12-ounce bottles with soda. For the machine to function properly, the standard deviation of the sample must be less than or equal to 0.02 ounce. A sample of 8 bottles is selected, and the number of ounces of soda in each bottle is given. At , can you reject the claim that the machine is functioning properly? Justify your answer. (Assume that the variables are approximately normally distributed.)
A) , ; There is evidence to reject the claim that the machine is working properly.
B) , ; There is evidence to reject the claim that the machine is working properly.
C) , ; There is not enough evidence to reject the claim that the machine is working properly.
D) , ; There is evidence to reject the claim that the machine is working properly.

Question

A machine fills 12-ounce bottles with soda. For the machine to function properly, the standard deviation of the sample must be less than or equal to 0.02 ounce. A sample of 8 bottles is selected, and the number of ounces of soda in each bottle is given. At  , can you reject the claim that the machine is functioning properly? Justify your answer. (Assume that the variables are approximately normally distributed.) 
A) , ; There is evidence to reject the claim that the machine is working properly. 
B) , ; There is evidence to reject the claim that the machine is working properly. 
C) , ; There is not enough evidence to reject the claim that the machine is working properly. 
D) , ; There is evidence to reject the claim that the machine is working properly.

Quizplus · Accepted Answer

We need to calculate the sample standard deviation and check whether it is less than or equal to 0.02. The sample standard deviation is calculated to be 0.0254, which is greater than 0.02. Therefore, we reject the claim that the machine is functioning properly at the 5% level of significance. The answer is D, as there is evidence to reject the claim that the machine is working properly.

A Machine Fills 12-Ounce Bottles with Soda