A study was undertaken to see how accurate food labeling for calories on food that is considered reduced calorie.: Expert Solutions for Success

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 table #Z.  Do the data indicate that at least two of the mean percent differences between the three groups are different?  Test at the 1% level.

Table #Z: Percent Differences Between Measured and Labeled Food

Let represents the mean percent difference of calories between measured and labeled reduced calorie foods that are nationally advertised.

Let represents the mean percent difference of calories between measured and labeled reduced calorie foods that are regionally distributed.

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

The objective of the problem is to test whether the data indicate that at least two of the mean percent differences between the three groups are different.

The null hypothesis is,

H₀: All three mean percentage differences are equal.

That is, ​

H₁: at least two of the mean percentage differences are not equal.

The level of significance used for this test is 1% =0.01

The level of significance, α=0.01.

F = 8.541533
p-value = 0.00193

Since p-value <0.01, we reject the null hypothesis.

The result is statistically significant at 0.1 level of significance. There is enough evidence to support the claim that there is at least two of the mean percent differences between the three groups are different.