Answered: The table to the right shows the cost…

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

The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At

alpha

equals0.01

can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances.

Very good stain removal	Good stain removal	Fair stain removal
0.35

0.42

0.44

0.51

2.74

1.28

0.64

0.46

0.34

1.62

0.33

nothing

0.47

0.75

nothing

0.36

1.32

nothing

(a) Identify the claim and state

Upper H 0

and

Upper H Subscript a

Choose the correct answer below.

Upper H 0

At least one mean is different from the others. (claim)

Upper H Subscript a

mu 1 equals mu 2 equals mu 3

Upper H 0

mu 1 equals mu 2 equals mu 3 equals mu 4 equals mu 5 equals mu 6

Upper H Subscript a

At least two means are different from the others. (claim)

Upper H 0

mu 1 equals mu 2 equals mu 3

Upper H Subscript a

At least one mean is different from the others. (claim)

Upper H 0

mu 1 equals mu 2 equals mu 3

(claim)

Upper H Subscript a

At least one mean is different from the others.

(b) Identify the degrees of freedom for the numerator and for the denominator, determine the critical value, and determine the rejection region.

The degrees of freedom for the numerator,

d.f. Subscript Upper N

nothing

and the degrees of freedom for the denominator,

d.f. Subscript Upper D

nothing

The critical value is

Upper F 0

equalsnothing

(Round to two decimal places as needed.)

The rejection region is

▼

greater than

less than

less than or equals

greater than or equals

nothing

(Round to two decimal places as needed.)

Fequals

nothing

(Round to three decimal places as needed.)

(d) Decide to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. Choose the correct decision below.

Since F is not in the rejection region, fail to reject

Upper H 0

Since F is not in the rejection region, reject

Upper H 0

Since F is in the rejection region, reject

Upper H 0

Since F is in the rejection region, fail to reject

Upper H 0

Choose the correct interpretation below.

There

▼

is not

enough evidence at the

significance level to

▼

dispute

support

the claim that the mean cost per ounce is

▼

the same for all three products

different for at least one product

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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