healthy food? The authors of a consumer research paper carried out a study to answer this question. They randomly assigned volunteers into one of three groups. The people in the first group were asked to taste a snack that was described as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from 1 (not at all hungry) to 7 (very hungry). The people in the third group were asked to rate their hunger but were not given a snack. The data in the table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger). Treatment Group Hunger Rating Sample Mean Sample Standard Deviation Healthy 5 8 7 4 7 3 4 7 6 5.6667 1.7321 Tasty 4 1 5 2 6 2 5 3 4 3.5556 1.6667 No Snack 3 4 5 6 5 6 2 4 4 4.3333 1.3229 Overall mean = 4.5185 (a) Do these data provide evidence that the mean hunger rating differs for at least two of the treatments ("healthy" snack, "tasty" snack, no snack)? Test the relevant hypotheses using a significance level of 0.05. Find the test statistic. (Round your test statistic to two decimal places.) F = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State the conclusion in the problem context. Reject H0. The data provide convincing evidence that the mean hunger rating is not the same for all three treatments.Fail to reject H0. The data do not provide convincing evidence that the mean hunger rating is not the same for all three treatments. Reject H0. The data do not provide convincing evidence that the mean hunger rating is not the same for all three treatments.Fail to reject H0. The data provide convincing evidence that the mean hunger rating is not the same for all three treatments. (b) Is it reasonable to conclude that the mean hunger rating is greater for people who do not get a snack? Explain. It is not reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the healthy snack group.It is reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the no snack group. It is not reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the tasty snack group.It is reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the tasty snack group.It is reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the healthy snack group.

healthy food? The authors of a consumer research paper carried out a study to answer this question. They randomly assigned volunteers into one of three groups. The people in the first group were asked to taste a snack that was described as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from 1 (not at all hungry) to 7 (very hungry). The people in the third group were asked to rate their hunger but were not given a snack. The data in the table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger). Treatment Group Hunger Rating Sample Mean Sample Standard Deviation Healthy 5 8 7 4 7 3 4 7 6 5.6667 1.7321 Tasty 4 1 5 2 6 2 5 3 4 3.5556 1.6667 No Snack 3 4 5 6 5 6 2 4 4 4.3333 1.3229 Overall mean = 4.5185 (a) Do these data provide evidence that the mean hunger rating differs for at least two of the treatments ("healthy" snack, "tasty" snack, no snack)? Test the relevant hypotheses using a significance level of 0.05. Find the test statistic. (Round your test statistic to two decimal places.) F = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State the conclusion in the problem context. Reject H0. The data provide convincing evidence that the mean hunger rating is not the same for all three treatments.Fail to reject H0. The data do not provide convincing evidence that the mean hunger rating is not the same for all three treatments. Reject H0. The data do not provide convincing evidence that the mean hunger rating is not the same for all three treatments.Fail to reject H0. The data provide convincing evidence that the mean hunger rating is not the same for all three treatments. (b) Is it reasonable to conclude that the mean hunger rating is greater for people who do not get a snack? Explain. It is not reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the healthy snack group.It is reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the no snack group. It is not reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the tasty snack group.It is reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the tasty snack group.It is reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the healthy snack group.

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

Do people feel hungrier after sampling a healthy food? The authors of a consumer research paper carried out a study to answer this question. They randomly assigned volunteers into one of three groups. The people in the first group were asked to taste a snack that was described as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from 1 (not at all hungry) to 7 (very hungry). The people in the third group were asked to rate their hunger but were not given a snack.

The data in the table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger).

Treatment Group	Hunger Rating	Sample Mean	Sample Standard Deviation
Healthy	5	8	7	4	7	3	4	7	6	5.6667	1.7321
Tasty	4	1	5	2	6	2	5	3	4	3.5556	1.6667
No Snack	3	4	5	6	5	6	2	4	4	4.3333	1.3229
Overall mean = 4.5185

(a)

Do these data provide evidence that the mean hunger rating differs for at least two of the treatments ("healthy" snack, "tasty" snack, no snack)? Test the relevant hypotheses using a significance level of 0.05.

Find the test statistic. (Round your test statistic to two decimal places.)

F =

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

State the conclusion in the problem context.

Reject H₀. The data provide convincing evidence that the mean hunger rating is not the same for all three treatments.Fail to reject H₀. The data do not provide convincing evidence that the mean hunger rating is not the same for all three treatments. Reject H₀. The data do not provide convincing evidence that the mean hunger rating is not the same for all three treatments.Fail to reject H₀. The data provide convincing evidence that the mean hunger rating is not the same for all three treatments.

(b)

Is it reasonable to conclude that the mean hunger rating is greater for people who do not get a snack? Explain.

It is not reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the healthy snack group.It is reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the no snack group. It is not reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the tasty snack group.It is reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the tasty snack group.It is reasonable to conclude that the mean hunger rating is greater for people who do not get a snack because the sample mean hunger rating is highest for the healthy snack group.

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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