To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material. Manufacturer 1 2 3 16 35 21 22 33 20 20 38 24 18 34 23 a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use . Compute the values below (to decimals, if necessary). Sum of Squares, Treatment Sum of Squares, Error Mean Squares, Treatment Mean Squares, Error Calculate the value of the test statistic (to decimals). The -value is - Select your answer -less than 0.01between 0.01 and 0.025between 0.025 and 0.05between 0.05 and 0.10greater than 0.10Item 6 What is your conclusion? - Select your answer -Conclude the mean time needed to mix a batch of material is not the same for all manufacturersDo not reject the assumption that mean time needed to mix a batch of material is the same for all manufacturersItem 7 b. At the level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers and . Calculate Fisher's LSD Value (to decimals). What conclusion can you draw after carrying out this test? - Select your answer -These manufacturers have different mean timesCannot conclude there is a difference in the mean time for these manufacturers

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter29: Tolerance, Clearance, And Interference

Section: Chapter Questions

Problem 16A: Spacers are manufactured to the mean dimension and tolerance shown in Figure 29-12. An inspector...

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To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material.

Manufacturer
	1	2	3
	16	35	21
	22	33	20
	20	38	24
	18	34	23

a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use .

Compute the values below (to decimals, if necessary).

Sum of Squares, Treatment
Sum of Squares, Error
Mean Squares, Treatment
Mean Squares, Error

Calculate the value of the test statistic (to decimals).

The -value is - Select your answer -less than 0.01between 0.01 and 0.025between 0.025 and 0.05between 0.05 and 0.10greater than 0.10Item 6

What is your conclusion?
- Select your answer -Conclude the mean time needed to mix a batch of material is not the same for all manufacturersDo not reject the assumption that mean time needed to mix a batch of material is the same for all manufacturersItem 7

b. At the level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers and .

Calculate Fisher's LSD Value (to decimals).

What conclusion can you draw after carrying out this test?
- Select your answer -These manufacturers have different mean timesCannot conclude there is a difference in the mean time for these manufacturers

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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