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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 9PT

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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.


1	2	3
15	26	23
21	24	22
19	29	26
17	25	25

a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use a=0.05

Compute the values below (to 2 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 2 decimals)._____

The p-value is _____

What is your conclusion? Choose: (Conclude the mean time needed to mix a batch of material is not the same for all manufacturers/Do not reject the assumption that mean time needed to mix a batch of material is the same for all manufacturers)

b. At the a=0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3.

Calculate Fisher's LSD Value (to 2 decimals). ____

What conclusion can you draw after carrying out this test? Choose ( These manufacturers have different mean times/Cannot conclude there is a difference in the mean time for these manufacturers)

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.
Compute the values below (to 2 decimals, if necessary).
Sum of Squares, Treatment
Sum of Squares, Error
Mean Squares, Treatment
= 0.05.
a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use a =
0000
Mean quares, Error
Calculate the value of the test statistic (to 2 decimals).
1
15
21
19
17
Manufacturer
What conclusion can you draw after carrying out this test?
- Select your answer -
2
26
24
29
25
3
23
22
26
25
The p-value is - Select your answer
What is your conclusion?
- Select your answer -
b. At the a = 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3.
Calculate Fisher's LSD Value (to 2 decimals).

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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