Suppose samples of six different brands of diet or imitation margarine were analyzed to determine the level of physiologically active polyunsaturated fatty acids (PAPUFA, in percent), resulting in the data shown in the accompanying table. Imperial 14.1 13.6 14.6 14.3   Parkay 12.8 12.5 13.6 13.0 12.3 Blue Bonnet 13.5 13.4 14.1 14.5   Chiffon 13.2 12.7 12.6 14   Mazola 16.8 17.3 16.4 17.3 18.0 Fleischmann's 18.1 17.2 18.8 18.4     (a) Test for differences among the true means for PAPUFA percentages among the different brands. Use  ? = 0.05. Calculate the test statistic. (Round your answer to two decimal places.) F =  Use technology to find the P-value. (Round your answer to four decimal places.) P-value =  What can you conclude? Reject H0. There is convincing evidence that the mean PAPUFA percentages for the six brands are not all equal.Fail to reject H0. There is convincing evidence that the mean PAPUFA percentages for the six brands are not all equal.    Reject H0. There is not convincing evidence that the mean PAPUFA percentages for the six brands are not all equal.Fail to reject H0. There is not convincing evidence that the mean PAPUFA percentages for the six brands are not all equal. (b)

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 + ...