A paper on men's and women's eating behaviors describes an experiment in which 74 men were assigned at random to one of four treatments. viewed slides of fit, muscular men viewed slides of fit, muscular men accompanied by diet and fitness-related text viewed slides of fit, muscular men accompanied by text not related to diet and fitness did not view any slides The participants then went to a room to complete a questionnaire. In this room, bowls of pretzels were set out on the tables. A research assistant noted how many pretzels were consumed by each participant while completing the questionnaire. Data consistent with summary quantities given in the paper are given in the table. Treatment 1 Treatment 2 Treatment 3 Treatment 4 8 7 1 7 7 8 5 2 4 0 2 5 13 4 0 7 2 9 3 5 1 8 0 2 5 6 3 0 8 2 4 0 12 7 4 3 5 8 5 4 1 8 5 2 0 5 8 4 6 14 8 1 4 9 4 1 12 0 0 7 6 6 0 3 3 12 12 5 6 10 8 6 2 10 Do these data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments? Test the relevant hypotheses using a significance level of 0.05. (Let ?1, ?2, ?3, and ?4 be the true mean number of pretzels consumed for the four different treatments.) State the appropriate null and alternative hypotheses. H0 : ?1 = ?2 = ?3 = ?4 Ha : all four of the ?i's are different H0 : all four of the ?i's are differentHa : ?1 = ?2 = ?3 = ?4 H0 : ?1 = ?2 = ?3 = ?4 Ha : at least two of the four ?i's are different H0 : at least two of the four ?i's are different Ha : ?1 = ?2 = ?3 = ?4 H0 : ?1 = ?2 = ?3 = ?4 Ha : at least three of the four ?i's are different Find the test statistic and P-value. Round your test statistic to two decimal places and your P-value to three decimal places.) F= P-value= State the conclusion in the problem context. We reject H0. The data do not provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments. We fail to reject H0. The data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments. We fail to reject H0. The data do not provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments. We reject H0. The data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments.

A paper on men's and women's eating behaviors describes an experiment in which 74 men were assigned at random to one of four treatments. viewed slides of fit, muscular men viewed slides of fit, muscular men accompanied by diet and fitness-related text viewed slides of fit, muscular men accompanied by text not related to diet and fitness did not view any slides The participants then went to a room to complete a questionnaire. In this room, bowls of pretzels were set out on the tables. A research assistant noted how many pretzels were consumed by each participant while completing the questionnaire. Data consistent with summary quantities given in the paper are given in the table. Treatment 1 Treatment 2 Treatment 3 Treatment 4 8 7 1 7 7 8 5 2 4 0 2 5 13 4 0 7 2 9 3 5 1 8 0 2 5 6 3 0 8 2 4 0 12 7 4 3 5 8 5 4 1 8 5 2 0 5 8 4 6 14 8 1 4 9 4 1 12 0 0 7 6 6 0 3 3 12 12 5 6 10 8 6 2 10 Do these data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments? Test the relevant hypotheses using a significance level of 0.05. (Let ?1, ?2, ?3, and ?4 be the true mean number of pretzels consumed for the four different treatments.) State the appropriate null and alternative hypotheses. H0 : ?1 = ?2 = ?3 = ?4 Ha : all four of the ?i's are different H0 : all four of the ?i's are differentHa : ?1 = ?2 = ?3 = ?4 H0 : ?1 = ?2 = ?3 = ?4 Ha : at least two of the four ?i's are different H0 : at least two of the four ?i's are different Ha : ?1 = ?2 = ?3 = ?4 H0 : ?1 = ?2 = ?3 = ?4 Ha : at least three of the four ?i's are different Find the test statistic and P-value. Round your test statistic to two decimal places and your P-value to three decimal places.) F= P-value= State the conclusion in the problem context. We reject H0. The data do not provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments. We fail to reject H0. The data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments. We fail to reject H0. The data do not provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments. We reject H0. The data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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1. A paper on men's and women's eating behaviors describes an experiment in which 74 men were assigned at random to one of four treatments.

viewed slides of fit, muscular men
viewed slides of fit, muscular men accompanied by diet and fitness-related text
viewed slides of fit, muscular men accompanied by text not related to diet and fitness
did not view any slides

The participants then went to a room to complete a questionnaire. In this room, bowls of pretzels were set out on the tables. A research assistant noted how many pretzels were consumed by each participant while completing the questionnaire. Data consistent with summary quantities given in the paper are given in the table.

Treatment 1	Treatment 2	Treatment 3	Treatment 4
8	7	1	7
7	8	5	2
4	0	2	5
13	4	0	7
2	9	3	5
1	8	0	2
5	6	3	0
8	2	4	0
12	7	4	3
5	8	5	4
1	8	5	2
0	5	8	4
6	14	8	1
4	9	4	1
12	0	0
7	6	6
0	3	3
12	12
	5
	6
	10
	8
	6
	2
	10

Do these data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments? Test the relevant hypotheses using a significance level of 0.05. (Let ?₁, ?₂, ?₃, and ?₄ be the true mean number of pretzels consumed for the four different treatments.)

State the appropriate null and alternative hypotheses.

H₀ : ?₁ = ?₂ = ?₃ = ?₄
H_a : all four of the ?_i's are different

H₀ : all four of the ?_i's are differentH_a : ?₁ = ?₂ = ?₃ = ?₄

H₀ : ?₁ = ?₂ = ?₃ = ?₄
H_a : at least two of the four ?_i's are different

H₀ : at least two of the four ?_i's are different

H_a : ?₁ = ?₂ = ?₃ = ?₄

H₀ : ?₁ = ?₂ = ?₃ = ?₄

H_a : at least three of the four ?_i's are different

Find the test statistic and P-value.

Round your test statistic to two decimal places and your P-value to three decimal places.)

P-value=

State the conclusion in the problem context.

We reject H₀. The data do not provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments.

We fail to reject H₀. The data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments.

We fail to reject H₀. The data do not provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments.

We reject H₀. The data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments.

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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Treatment 1	Treatment 2	Treatment 3	Treatment 4
8	7	1	7
7	8	5	2
4	0	2	5
13	4	0	7
2	9	3	5
1	8	0	2
5	6	3	0
8	2	4	0
12	7	4	3
5	8	5	4
1	8	5	2
0	5	8	4
6	14	8	1
4	9	4	1
12	0	0
7	6	6
0	3	3
12	12
	5
	6
	10
	8
	6
	2
	10

Treatment 1	Treatment 2	Treatment 3	Treatment 4
8	7	1	7
7	8	5	2
4	0	2	5
13	4	0	7
2	9	3	5
1	8	0	2
5	6	3	0
8	2	4	0
12	7	4	3
5	8	5	4
1	8	5	2
0	5	8	4
6	14	8	1
4	9	4	1
12	0	0
7	6	6
0	3	3
12	12
	5
	6
	10
	8
	6
	2
	10

Treatment 1	Treatment 2	Treatment 3	Treatment 4
8	7	1	7
7	8	5	2
4	0	2	5
13	4	0	7
2	9	3	5
1	8	0	2
5	6	3	0
8	2	4	0
12	7	4	3
5	8	5	4
1	8	5	2
0	5	8	4
6	14	8	1
4	9	4	1
12	0	0
7	6	6
0	3	3
12	12
	5
	6
	10
	8
	6
	2
	10