The table to the right shows the number of female students who played on a sports team in grades 9 through 12 for a random sample of 6 high schools in a state. At α=0.10, can you reject the claim that the mean numbers of female students who played on a sports team are equal for all grades? 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. 9 Grade 10 Grade 11 Grade 12 64 51 56 49 53 58 46 42 133 125 115 102 112 106 87 84 82 77 86 65 83 79 77 75 (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 one mean is 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=μ4 (claim) Ha: At least one mean is different from the others. D. H0: μ1=μ2=μ3=μ4 Ha: At least one mean is different from the others. (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, fail to reject H0. B. Since F is in the rejection region, reject H0. C. Since F is in the rejection region, fail to reject H0. D. Since F is not in the rejection region, reject H0. Interpret the decision in the context of the original claim. There______ is or is not enough evidence at the 10% significance level to____ dispute or support the claim that the mean numbers of female students who played on a sports team is____ the same for all grades or different for at least one grade

The table to the right shows the number of female students who played on a sports team in grades 9 through 12 for a random sample of 6 high schools in a state. At α=0.10, can you reject the claim that the mean numbers of female students who played on a sports team are equal for all grades? 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. 9 Grade 10 Grade 11 Grade 12 64 51 56 49 53 58 46 42 133 125 115 102 112 106 87 84 82 77 86 65 83 79 77 75 (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 one mean is 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=μ4 (claim) Ha: At least one mean is different from the others. D. H0: μ1=μ2=μ3=μ4 Ha: At least one mean is different from the others. (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, fail to reject H0. B. Since F is in the rejection region, reject H0. C. Since F is in the rejection region, fail to reject H0. D. Since F is not in the rejection region, reject H0. Interpret the decision in the context of the original claim. There is or is not enough evidence at the 10% significance level to dispute or support the claim that the mean numbers of female students who played on a sports team is the same for all grades or different for at least one grade

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 number of female students who played on a sports team in grades 9 through 12 for a random sample of 6 high schools in a state. At

α=0.10,

can you reject the claim that the mean numbers of female students who played on a sports team are equal for all grades? 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.

9	Grade 10	Grade 11	Grade 12
64	51	56	49
53	58	46	42
133	125	115	102
112	106	87	84
82	77	86	65
83	79	77	75

(a) Identify the claim and state

and

Ha.

Choose the correct answer below.

H0:

μ1=μ2=μ3=μ4=μ5=μ6

Ha:

At least one mean is 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=μ4 (claim)

Ha:

At least one mean is different from the others.

H0:

μ1=μ2=μ3=μ4

Ha:

At least one mean is different from the others. (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,

fail to reject

H0.

Since F

in the rejection region,

reject

H0.

Since F

in the rejection region,

fail to reject

H0.

Since F

is not

in the rejection region,

reject

H0.

Interpret the decision in the context of the original claim.

There______

is not

enough evidence at the

10%

significance level to____

dispute or support

the claim that the mean numbers of female students who played on a sports team is____

the same for all grades

different for at least one grade

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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