Healthy Eating Americans appear to be eating healthier. Between  1970 and 2007  the per capita consumption of broccoli increased  1000% from 0.5  to 5.5 pounds. A nutritionist followed a group of people randomly assigned to one of three groups and noted their monthly broccoli intake (in pounds). At α=0.10 , is there a difference in means?   Group A Group B Group C 1.9 4.1 2.3 2 4.2 2.5 1 4.3 3.4 1.1 4.5 3.4 1.2 3.3 4.1 1.3 3.4 1.5       State the hypotheses and identify the claim with the correct hypothesis. H0:μ1=μ2=μ3 claim/do not claim ▼(Choose one) H1: At least one mean is different from the others. claim/not claim▼(Choose one)       Find the critical value. Use The F Distribution Table to find the critical value. Round the answer to two decimal places. The critical value is  Compute the test value. Round the intermediate and the final answers to two decimal places.   F= Make the decision. reject/do not reject▼(Choose one) the null hypothesis.       Summarize the results. There is/is not  ▼(Choose one) enough evidence to support the claim that there exists a difference in mean broccoli consumption among the three groups.

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 + ...