At a Large Automobile Factory,four Different Machines Are Used to Produce

question 7

Multiple Choice

At a large automobile factory,four different machines are used to produce disc brakes.To make sure that the disc brakes are all being produced with comparable diameters,daily samples of 16 disc brakes are taken from the production lines of each of the four machines and their diameters measured.The deviation from the goal diameter of 322 micrometers is measured to the nearest micrometer.Assume that the distribution of these deviations is approximately Normal with a common standard deviation.Does it appear that disc brakes made on the four machines are made with equal mean diameters? SPSS output is included below. Some summary measures for the four machines are given below. Suppose we are interested in the contrast that compares the average of machines 1,3,and 4 (the most recently purchased machines) to machine 2 (a slightly older model) .

Do the data show evidence of a violation of the assumption that the four populations have the same standard deviation?

• A)Yes,because 124.47/48.84 is greater than 2
• B)Yes,because the variation decreases when we move from machine 1 to machine 4
• C)No,because 11.16/6.99 is smaller than 2
• D)No,because the sample sizes are all equal

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Definitions:

Correlation Coefficients

Statistical measures that indicate the extent to which two or more variables fluctuate together, ranging from -1 to 1, where 1 indicates a perfect positive correlation and -1 indicates a perfect negative correlation.

Cause and Effect

A relationship between events or things, where one is the result of the other or others, a combination of action and reaction.

Negatively Correlated

Describes a relationship between two variables where one variable increases as the other decreases.

Risk of Cancer

The probability or chance that an individual will develop cancer over a certain period of time, often influenced by genetic, environmental, and lifestyle factors.