A study was undertaken to see how accurate food labeling for calories on food that is considered "reduced calorie". The group measured the amount of calories for each item of food and then found the percent difference between measured and labeled food. The group also looked at food that was nationally advertised, regionally distributed, or locally prepared. The data is in the following table ("Calories datafile," 2013). Table: Percent Differences Between Measured and Labeled Food National Advertised Regionally Distributed Locally Prepared 2 41 15 -28 46 60 -6 2 250 8 25 145 6 39 6 -1 16.5 80 10 17 95 13 28 3 15 -3 -4 14 -4 34 -18 42 10 5 3 -7 3 -0.5 -10 6 Do the data indicate that at least two of the mean percent differences between the three groups are different? Test at the 10% level. ********************************************************************** Let x1 = percent difference of calories between measured and labeled reduced calorie food that is nationally advertised Let x2 = percent difference of calories between measured and labeled reduced calorie food that is regionally distributed Let x3 = percent difference of calories between measured and labeled reduced calorie food that is prepared locally. Let μ1 = mean percent difference of calories between measured and labeled reduced calorie foods that are nationally advertised Let μ2 = mean percent difference of calories between measured and labeled reduced calorie foods that are regionally distributed Let μ3 = mean percent difference of calories between measured and labeled reduced calorie foods that are prepared locally. (vii) Determine F ratio test statistic and corresponding p-value. Use "CTRL-click" to access link. Enter test statistic to nearest hundredth, then enter comma, then enter p-value to nearest ten-thousandth. Examples of correctly entered responses: 12.33,0.0040 7.50,0.0001 6.77,0.5049 (viii) Comparing p-value and α value, which is the correct decision to make for this hypothesis test? A. Accept HA B. Fail to reject Ho C. Accept Ho D. Reject Ho Enter letter corresponding to correct answer. (ix) Select the statement that most correctly interprets the result of this test: A. The result is not statistically significant at .10 level of significance. Sufficient evidence exists to support the claim that at least two of the mean percent differences between the three groups are different. B. The result is statistically significant at .10 level of significance. There is not enough evidence to support the claim that at least two of the mean percent differences between the three groups are different. C. The result is statistically significant at .10 level of significance. Sufficient evidence exists to support the claim that at least two of the mean percent differences between the three groups are different. D. The result is not statistically significant at .10 level of significance. There is not enough evidence to support the claim that at least two of the mean percent differences between the three groups are different.

A study was undertaken to see how accurate food labeling for calories on food that is considered "reduced calorie". The group measured the amount of calories for each item of food and then found the percent difference between measured and labeled food. The group also looked at food that was nationally advertised, regionally distributed, or locally prepared. The data is in the following table ("Calories datafile," 2013). Table: Percent Differences Between Measured and Labeled Food National Advertised Regionally Distributed Locally Prepared 2 41 15 -28 46 60 -6 2 250 8 25 145 6 39 6 -1 16.5 80 10 17 95 13 28 3 15 -3 -4 14 -4 34 -18 42 10 5 3 -7 3 -0.5 -10 6 Do the data indicate that at least two of the mean percent differences between the three groups are different? Test at the 10% level. ********************************************************************** Let x1 = percent difference of calories between measured and labeled reduced calorie food that is nationally advertised Let x2 = percent difference of calories between measured and labeled reduced calorie food that is regionally distributed Let x3 = percent difference of calories between measured and labeled reduced calorie food that is prepared locally. Let μ1 = mean percent difference of calories between measured and labeled reduced calorie foods that are nationally advertised Let μ2 = mean percent difference of calories between measured and labeled reduced calorie foods that are regionally distributed Let μ3 = mean percent difference of calories between measured and labeled reduced calorie foods that are prepared locally. (vii) Determine F ratio test statistic and corresponding p-value. Use "CTRL-click" to access link. Enter test statistic to nearest hundredth, then enter comma, then enter p-value to nearest ten-thousandth. Examples of correctly entered responses: 12.33,0.0040 7.50,0.0001 6.77,0.5049 (viii) Comparing p-value and α value, which is the correct decision to make for this hypothesis test? A. Accept HA B. Fail to reject Ho C. Accept Ho D. Reject Ho Enter letter corresponding to correct answer. (ix) Select the statement that most correctly interprets the result of this test: A. The result is not statistically significant at .10 level of significance. Sufficient evidence exists to support the claim that at least two of the mean percent differences between the three groups are different. B. The result is statistically significant at .10 level of significance. There is not enough evidence to support the claim that at least two of the mean percent differences between the three groups are different. C. The result is statistically significant at .10 level of significance. Sufficient evidence exists to support the claim that at least two of the mean percent differences between the three groups are different. D. The result is not statistically significant at .10 level of significance. There is not enough evidence to support the claim that at least two of the mean percent differences between the three groups are different.

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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Table: Percent Differences Between Measured and Labeled Food

National Advertised	Regionally Distributed	Locally Prepared
2	41	15
-28	46	60
-6	2	250
8	25	145
6	39	6
-1	16.5	80
10	17	95
13	28	3
15	-3
-4	14
-4	34
-18	42
10
5
3
-7
3
-0.5
-10
6

Do the data indicate that at least two of the mean percent differences between the three groups are different? Test at the 10% level.

**********************************************************************

Let x₁= percent difference of calories between measured and labeled reduced calorie food that is nationally advertised

Let x₂= percent difference of calories between measured and labeled reduced calorie food that is regionally distributed

Let x₃= percent difference of calories between measured and labeled reduced calorie food that is prepared locally.

Let μ₁= mean percent difference of calories between measured and labeled reduced calorie foods that are nationally advertised

Let μ₂= mean percent difference of calories between measured and labeled reduced calorie foods that are regionally distributed

Let μ₃= mean percent difference of calories between measured and labeled reduced calorie foods that are prepared locally.

(vii) Determine F ratio test statistic and corresponding p-value.

Use "CTRL-click" to access link. Enter test statistic to nearest hundredth, then enter comma, then enter p-value to nearest ten-thousandth. Examples of correctly entered responses:

12.33,0.0040

7.50,0.0001

6.77,0.5049

(viii) Comparing p-value and α value, which is the correct decision to make for this hypothesis test?

A. Accept H_A

B. Fail to reject H_o

C. Accept H_o

D. Reject H_o

Enter letter corresponding to correct answer.

(ix) Select the statement that most correctly interprets the result of this test:

A. The result is not statistically significant at .10 level of significance. Sufficient evidence exists to support the claim that at least two of the mean percent differences between the three groups are different.

B. The result is statistically significant at .10 level of significance. There is not enough evidence to support the claim that at least two of the mean percent differences between the three groups are different.

C. The result is statistically significant at .10 level of significance. Sufficient evidence exists to support the claim that at least two of the mean percent differences between the three groups are different.

D. The result is not statistically significant at .10 level of significance. There is not enough evidence to support the claim that at least two of the mean percent differences between the three groups are different.

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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