The Makers of Mini-Oats Cereal Have an Automated Packaging Machine

question 109

Multiple Choice

The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces.Every box of cereal is not expected to contain exactly the targeted weight,but the average of all boxes filled should.At the end of every shift (eight hours) ,16 boxes are selected at random and the mean and standard deviation of the sample are computed.Based on these sample results,the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate.At the end of a particular shift during which the machine was filling 24-ounce boxes of Mini-Oats,the sample mean of 16 boxes was 24.32 ounces,with a standard deviation of 0.70 ounce.Assist the production control manager in determining if the machine is achieving its targeted average using test statistic and critical value t.Conduct the test using a p-value.

• A)p-value = 0.0872 > 0.025;therefore do not reject H₀
• B)p-value = 0.0422 > 0.005;therefore do not reject H₀
• C)p-value = 0.0314 < 0.105;therefore reject H₀
• D)p-value = 0.0121< 0.0805;therefore reject H₀

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Definitions:

Counting Method

A mathematical technique used to determine the total number of possible outcomes in a given situation.

Count And Divide

A method involving enumeration and separation into parts or groups, typically used for analytical or problem-solving purposes.

Intuitive Judgment

The ability to understand or know something without the need for conscious reasoning or direct evidence.

Bias

A tendency to favor or lean towards a particular perspective, judgment, or result over others, often in a way considered to be unfair.