(a) Identify the claim and state H0 and Ha. Choose the correct answer below. A. H0: μ1=μ2=μ3=μ4=μ5=μ6 Ha: At least two means are different from the others. (claim) B. H0: At least one mean is different from the others. (claim) Ha: μ1=μ2=μ3=μ4=μ5=μ6 C. H0: μ1=μ2=μ3 Ha: At least one mean is different from the others. (claim) D. H0: μ1=μ2=μ3 (claim) (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.N, is __, and the degrees of freedom for the denominator, d.f.D, is _. The critical value is F0=. (Round to two decimal places as needed.) The rejection region is F greater than or equals≥ less than or equals≤ less than< greater than> _. (Round to two decimal places as needed.) (c) Calculate the test statistic. F= (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. A. Since F is not in the rejection region, reject H0. B. Since F is not in the rejection region, fail to reject H0. C. Since F is in the rejection region, fail to reject H0. D. Since F is in the rejection region, reject H0. Choose the correct interpretation below. There is not or is enough evidence at the 2.5% significance level to dispute or support the claim that the mean cost per ounce is the same for all three products or different for at least one product

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 4CYU

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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

α=0.025,

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
0.37	0.58	0.34
0.51	2.74	1.25
0.33	0.98	0.44
1.47	0.42
0.49	0.46
0.48	1.31

(a) Identify the claim and state

and

Ha.

Choose the correct answer below.

H0:

μ1=μ2=μ3=μ4=μ5=μ6

Ha:

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

H0:

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

Ha:

μ1=μ2=μ3=μ4=μ5=μ6

H0:

μ1=μ2=μ3

Ha:

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

H0:

μ1=μ2=μ3

(claim)

(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.N,

____,

and the degrees of freedom for the denominator,

d.f.D,

_____.

The critical value is

F0=.

(Round to two decimal places as needed.)

The rejection region is

greater than or equals≥

less than or equals≤

less than<

greater than>

___.

(Round to two decimal places as needed.)

(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, reject

H0.

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

H0.

Since F is in the rejection region, fail to reject

H0.

Since F is in the rejection region, reject

H0.

Choose the correct interpretation below.

There

is not

enough evidence at the

2.5%

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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