A Machine Fills 12 -Ounce Bottles with Soda $0.02$ Ounce a Sample of 8 Bottles Is Selected, and the Machine

question 115

Multiple Choice

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 $\alpha = 0.05$ , can you reject the claim that the machine is functioning properly? Justify your answer. (A that the variables are approximately normally distributed.)
$$\begin{array} { l l l l } 12.04 & 11.91 & 11.91 & 11.91 \\11.91 & 11.97 & 12.01 & 12.06\end{array}$$

• A) \(\chi ^ { 2 } = 72.000 , \chi _ { \text {critical } } ^ { 2 } = 14.067\); There is evidence to reject the claim that the machine is working properly.
• B) \(\chi ^ { 2 } = 65.570 , \chi _ { \text {critical } } ^ { 2 } = 15.507\); There is not enough evidence to reject the claim that the machine is working properly.
• C) \(\chi ^ { 2 } = 72.000 , \chi _ { \text {critical } } ^ { 2 } = 15.507\); There is evidence to reject the claim that the machine is working properly.
• D) \(\chi ^ { 2 } = 65.570 , \chi _ { \text {critical } } ^ { 2 } = 14.067\); There is evidence to reject the claim that the machine is working properly.

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Definitions:

Percentage of Defects

A quality measure indicating the proportion of defective items in a production run or sample.

On-time Deliveries

The performance metric that measures the percentage of orders delivered to the customer within the agreed-upon delivery time.

Organizational Architecture

The structure of an organization. Consists of the assignment of decision rights within the organization, the methods of rewarding individuals, and the systems to evaluate the performance of both individuals and business units.

Product Redesign

The process of changing or updating a product’s features, performance, or aesthetics to meet new market demands or improve efficiency.