Suppose the following data show the percentage of 17- to 24-year-olds who are attending college in several metropolitan statistical areas in four geographic regions of the United States. Northeast Midwest South West 28.2 35.9 59.1 16.4 39.4 32.8 37.9 34.1 32.7 23.1 28.0 23.1 46.5 43.9 41.6 11.9 32.5 32.5 34.0 44.2 14.1 57.7 19.5 27.3 36.2 30.7 30.6 56.9 36.9 64.4 66.8 14.3 38.3 27.6 32.7 36.8 57.6 56.3 30.4 28.7 60.7 78.3 38.3 17.9 42.0 29.5 32.5 75.5 30.3 52.8 35.7 22.9 51.0 28.9 34.5 25.9 60.4 24.3 29.2 58.3 54.6 27.4 21.8 30.5 31.0 28.3 42.4 23.2 25.5 70.7 34.9 74.2 22.0 32.9 37.1 30.1 37.4 29.0 30.3 34.0 26.6 21.2 29.5 32.4 31.7 22.0 56.6 38.5 28.4 39.7 34.1 36.0 39.2 21.8 39.0 35.2 26.8 32.6 Use ? = 0.05 to test whether the mean percentage of 17- to 24-year-olds who are attending college is the same for the four geographic regions. State the null and alternative hypotheses. H0: μN = μM = μS = μW Ha: Not all the population means are equal. H0: At least two of the population means are equal. Ha: At least two of the population means are different. H0: μN ≠ μM ≠ μS ≠ μW Ha: μN = μM = μS = μW H0: μN = μM = μS = μW Ha: μN ≠ μM ≠ μS ≠ μW H0: Not all the population means are equal. Ha: μN = μM = μS = μW Find the value of the test statistic. (Round your answer to two decimal places.) =____ Find the p-value. (Round your answer to three decimal places.) p-value = _____ State your conclusion. (A) Reject H0. There is not sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions. (B) Do not reject H0. There is sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions. (C) Do not reject H0. There is not sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions. (D) Reject H0. There is sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions.

Suppose the following data show the percentage of 17- to 24-year-olds who are attending college in several metropolitan statistical areas in four geographic regions of the United States. Northeast Midwest South West 28.2 35.9 59.1 16.4 39.4 32.8 37.9 34.1 32.7 23.1 28.0 23.1 46.5 43.9 41.6 11.9 32.5 32.5 34.0 44.2 14.1 57.7 19.5 27.3 36.2 30.7 30.6 56.9 36.9 64.4 66.8 14.3 38.3 27.6 32.7 36.8 57.6 56.3 30.4 28.7 60.7 78.3 38.3 17.9 42.0 29.5 32.5 75.5 30.3 52.8 35.7 22.9 51.0 28.9 34.5 25.9 60.4 24.3 29.2 58.3 54.6 27.4 21.8 30.5 31.0 28.3 42.4 23.2 25.5 70.7 34.9 74.2 22.0 32.9 37.1 30.1 37.4 29.0 30.3 34.0 26.6 21.2 29.5 32.4 31.7 22.0 56.6 38.5 28.4 39.7 34.1 36.0 39.2 21.8 39.0 35.2 26.8 32.6 Use ? = 0.05 to test whether the mean percentage of 17- to 24-year-olds who are attending college is the same for the four geographic regions. State the null and alternative hypotheses. H0: μN = μM = μS = μW Ha: Not all the population means are equal. H0: At least two of the population means are equal. Ha: At least two of the population means are different. H0: μN ≠ μM ≠ μS ≠ μW Ha: μN = μM = μS = μW H0: μN = μM = μS = μW Ha: μN ≠ μM ≠ μS ≠ μW H0: Not all the population means are equal. Ha: μN = μM = μS = μW Find the value of the test statistic. (Round your answer to two decimal places.) = Find the p-value. (Round your answer to three decimal places.) p-value = _ State your conclusion. (A) Reject H0. There is not sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions. (B) Do not reject H0. There is sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions. (C) Do not reject H0. There is not sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions. (D) Reject H0. There is sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

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Section: Chapter Questions

Problem 11.1EP

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Suppose the following data show the percentage of 17- to 24-year-olds who are attending college in several metropolitan statistical areas in four geographic regions of the United States.

Northeast	Midwest	South	West
28.2	35.9	59.1	16.4
39.4	32.8	37.9	34.1
32.7	23.1	28.0	23.1
46.5	43.9	41.6	11.9
32.5	32.5	34.0	44.2
14.1	57.7	19.5	27.3
36.2	30.7	30.6	56.9
36.9	64.4	66.8	14.3
38.3	27.6	32.7	36.8
57.6	56.3	30.4	28.7
60.7	78.3	38.3	17.9
	42.0	29.5	32.5
	75.5	30.3	52.8
	35.7	22.9	51.0
	28.9	34.5	25.9
	60.4	24.3	29.2
	58.3	54.6	27.4
	21.8	30.5	31.0
	28.3	42.4	23.2
	25.5	70.7	34.9
	74.2	22.0	32.9
	37.1	30.1	37.4
	29.0	30.3	34.0
	26.6	21.2	29.5
	32.4	31.7	22.0
	56.6	38.5
	28.4	39.7
	34.1	36.0
	39.2	21.8
	39.0	35.2
		26.8
		32.6

Use ? = 0.05 to test whether the mean percentage of 17- to 24-year-olds who are attending college is the same for the four geographic regions.

State the null and alternative hypotheses.

H₀: μ_N = μ_M = μ_S = μ_W
H_a: Not all the population means are equal.

H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

H₀: μ_N ≠ μ_M ≠ μ_S ≠ μ_W
H_a: μ_N = μ_M = μ_S = μ_W

H₀: μ_N = μ_M = μ_S = μ_W
H_a: μ_N ≠ μ_M ≠ μ_S ≠ μ_W

H₀: Not all the population means are equal.
H_a: μ_N = μ_M = μ_S = μ_W

Find the value of the test statistic. (Round your answer to two decimal places.) =____

Find the p-value. (Round your answer to three decimal places.)

p-value = _____

State your conclusion.

(A) Reject H₀. There is not sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions.

(B) Do not reject H₀. There is sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions.

(C) Do not reject H₀. There is not sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions.

(D) Reject H₀. There is sufficient evidence to conclude that the percentage of 17- to 24-year-olds who are attending college is not the same for the four geographic regions.

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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