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 2, 28, 6, 8, 6, 1, 10, 13, 15, 4, 4, 18, 10, 5, 3, 7, 3, 0 5, 10, 6 Regionally Distributed 41, 46, 2, 25, 39, 16 5, 17, 28, 3, 14, 34, 42 Locally Prepared 15, 60, 250, 145, 6, 80, 95, 3 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 x 1 percent difference of calories between measured and labeled reduced calorie food that is nationally advertised Let x 2 percent difference of calories between measured and labeled reduced calorie food that is regionally distributed Let x 3 percent difference of calories between measured and labeled reduced calorie food that is prepared locally Let 1 mean percent difference of calories between measured and labeled reduced calorie foods that are nationally advertised Let 2 mean percent difference of calories between measured and labeled reduced calorie foods that are regionally distributed Let 3 mean percent difference of calories between measured and labeled reduced calorie foods that are prepared locally (i)Which of the following statements correctly defines the null hypothesis H O A None of the three mean percentage differences are equal B At least two of the mean percentage differences are not equal C At least two of the mean percentage differences are equal D All three mean percentage differences are equal Let 1 mean percent difference of calories between measured and labeled reduced calorie foods that are nationally advertised Let 2 mean percent difference of calories between measured and labeled reduced calorie foods that are regionally distributed Let 3 mean percent difference of calories between measured and labeled reduced calorie foods that are prepared locally (ii)Which of the following statements correctly defines the alternative hypothesis H A A None of the three mean percentage differences are equal B At least two of the mean percentage differences are not equal C At least two of the mean percentage differences are equal D All three mean percentage differences are equal (iii)Enter the level of significance used for this test (iii)Calculate sample mean and sample standard deviation for sample percent differences between measured and labeled food that is advertised nationally (v) Calculate sample mean and sample standard deviation for for sample percent differences between measured and labeled food that is distributed regionally (vi)Calculate sample mean and sample standard deviation for sample percent differences between measured and labeled food that is prepared locally (vii)Determine F ratio test statistic and corresponding p value (viii)Comparing p value and 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 (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 claimthat at least two of the mean percent differences between the three groups are different

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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

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

2, -28, -6, 8, 6, -1, 10, 13, 15, -4, -4, -18, 10, 5, 3, -7, 3, -0.5, -10, 6

Regionally Distributed

41, 46, 2, 25, 39, 16.5, 17, 28, -3, 14, 34, 42

Locally Prepared

15, 60, 250, 145, 6, 80, 95, 3

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

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Letx₁= percent difference of calories between measured and labeled reduced calorie food that is nationally advertised

Letx₂= percent difference of calories between measured and labeled reduced calorie food that is regionally distributed

Letx₃= percent difference of calories between measured and labeled reduced calorie food that is prepared locally.

Let₁= mean percent difference of calories between measured and labeled reduced calorie foods that are nationally advertised

Let₂= mean percent difference of calories between measured and labeled reduced calorie foods that are regionally distributed

Let₃= mean percent difference of calories between measured and labeled reduced calorie foods that are prepared locally.

(i)Which of the following statements correctly defines the null hypothesisH_O?

A.None of the three mean percentage differences are equal

B.At least two of the mean percentage differences are not equal

C.At least two of the mean percentage differences are equal

D.All three mean percentage differences are equal

Let₁= mean percent difference of calories between measured and labeled reduced calorie foods that are nationally advertised

Let₂= mean percent difference of calories between measured and labeled reduced calorie foods that are regionally distributed

Let₃= mean percent difference of calories between measured and labeled reduced calorie foods that are prepared locally.

(ii)Which of the following statements correctly defines the alternative hypothesisH_A?

A.None of the three mean percentage differences are equal

B.At least two of the mean percentage differences are not equal

C.At least two of the mean percentage differences are equal

D.All three mean percentage differences are equal

(iii)Enter the level of significanceused for this test:

(iii)Calculate sample mean and sample standard deviation for sample percent differences between measured and labeled food that is advertised nationally.

(v)Calculate sample mean and sample standard deviation for for sample percent differences between measured and labeled food that is distributed regionally.

(vi)Calculate sample mean and sample standard deviation for sample percent differences between measured and labeled food that is prepared locally.

(vii)DetermineFratio test statistic and corresponding p-value.

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

A.AcceptH_A

B.Fail to rejectH_o

C.AcceptH_o

D.RejectH_o

(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 claimthat at least two of the mean percent differences between the three groups are different.