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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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Question

Random sampling from four normally distributed populations produced the following data: (You may find it useful to reference the F table.)

a. Calculate the grand mean. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Grand mean =

b. Calculate SSTR and MSTR. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

SSTR =

MSTR =

c. Calculate SSE and MSE. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

SSE =

MSE =

d. Specify the competing hypotheses in order to determine whether some differences exist between the population means.

(Which one is correct below)

H₀: μ_A ≥ μ_B ≥ μ_C; H_A: Not all population means are equal.
H₀: μ_A = μ_B = μ_C; H_A: Not all population means are equal.
H₀: μ_A ≤ μ_B ≤ μ_C; H_A: Not all population means are equal.

e-1. Calculate the value of the F_{(df1, df2)} test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test statistic =

e-2. Find the p-value.

(Which one is correct below)

0.01 ≤ p-value < 0.025
0.05 ≤ p-value < 0.10
p-value < 0.01
p-value ≥ 0.10
0.025 ≤ p-value < 0.05

f. At the 10% significance level, what is the conclusion to the test?

(Which one is correct below)

Do not reject H₀ since the p-value is not less than significance level
Reject H₀ since the p-value is less than significance level
Reject H₀ since the p-value is not less than significance level
Do not reject H₀ since the p-value is less than significance level

g. Interpret the results at α = 0.10.
(Which one is correct below)

We conclude that some means differ.
We cannot conclude that some means differ.
We cannot conclude that all means differ.
We cannot conclude that population mean C is greater than population mean A.

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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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