To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.Temperature 50°C60°C70°C 312827 212932 333232 362134 292535 a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary). Source of VariationSum of SquaresDegrees of FreedomMean SquareFp-valueTreatments Error Total b. Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process.Calculate the value of the test statistic (to 2 decimals). _________The P-value is What is your conclusion? _____________

Temperature50°C60°C70°C312827212932333232362134292535

Answered: To study the effect of temperature on…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.

Temperature
	50°C	60°C	70°C
	31	28	27
	21	29	32
	33	32	32
	36	21	34
	29	25	35

a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary).

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments
Error
Total

b. Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process.

Calculate the value of the test statistic (to 2 decimals). _________

The P-value is

What is your conclusion? _____________

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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