Provide an Appropriate Response Is There Evidence at The $\alpha = 0.01$

question 39

Multiple Choice

Provide an appropriate response.
-A soda machine is set to fill bottles with 24 ounces of cola. As part of a quality control program, an inspector records the amount of fill over or under 24 ounces for one minute. His observations are shown below.
$\begin{array} { r r r r r r r r r r } - 0.40 & - 0.45 & - 0.21 & - 0.15 & - 0.71 & - 0.05 & - 0.84 & - 0.12 & - 0.05 & - 0.58 \\ - 0.97 & - 1.01 & - 0.75 & 0.50 & 0.08 & - 0.45 & - 0.27 & - 0.75 & - 0.07 & - 1.00 \\ 0.25 & 0.25 & 0.91 & 0.99 & 0.36 & 0.05 & 0.11 & 0.31 & 0.84 & 0.67 \\ 0.45 & 0.60 & 0.01 & 0.98 & 0.22 & 0.72 & 0.77 & 0.48 & 0.13 & 0.39 \\ - 0.73 & - 0.78 & - 0.90 & - 0.14 & - 0.68 & 0.80 & 0.12 & 0.16 & 0.37 & 0.27 \end{array}$
Is there evidence at the $\alpha = 0.01$ level of significance to support the hypothesis that the filling process is not random with respect to amounts over and under 24 ounces?

• A) \(z = - 5.71\)
• Since \(| \mathrm { z } | > \mathrm { z } _ { 0 } .005 = 2.58\), we reject \(\mathrm { H } _ { 0 }\). There is sufficient evidence to support the hypothesis that the filling process is not random.
• B) \(z = - 6.28\)
• Since \(| \mathrm { z } | > \mathrm { z } 0.005 = 2.58\), we reject \(\mathrm { H } _ { 0 }\). There is sufficient evidence to support the hypothesis that the filling process is not random.
• C) \(\mathrm { z } = - 1.25\)
• Since \(| z | < z _ { 0.005 } = 2.58\), we do not reject \(\mathrm { H } _ { 0 }\). There is not sufficient evidence to support the hypothesis that the filling process is not random.
• D) \(z = 0.67\)
• Since \(| z | < z _ { 0.005 } = 2.58\), we do not reject \(H _ { 0 }\). There is not sufficient evidence to support the hypothesis that the filling process is not random.

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Definitions:

Balance of Trade

The difference between the monetary value of a nation's exports and imports over a certain period. A positive balance means more goods were exported than imported, and vice versa.

World Trade Organization

An international body that deals with the rules of trade between nations, aiming to ensure trade flows as smoothly and predictably as possible.

Multilateral Forum

A platform where three or more countries engage in dialogue and collaboration on issues of common interest.

Quotas

Limits set by governments on the amount of a specific good that can be imported or exported within a certain timeframe.