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

question 176

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:

Standard Normal Random Variable

A type of random variable that has a mean of 0 and a standard deviation of 1, following the standard normal distribution.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the values differ from the mean of the data set.

Negative Value

A negative value represents a number less than zero, often indicating a deficit or reduction in mathematical and statistical contexts.

Normal Distribution

A bell-shaped probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence.