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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