A certain vending company's soft-drink dispensing machines are supposed to serve 6 oz of beverage. Various machines were sampled, and the resulting amounts of dispensed drink (in ounces) were recorded, as shown in the following table. Does this sample evidence provide sufficient reason to reject the null hypothesis that all five machines dispense the same average amount of soft drink? Use ? = .01? Machines     A         B         C         D         E     4.5 7.0 3.9 6.4 5.5 4.1 7.2 4.1 6.5 5.8 4.5 7.1 4.5 6.2 4.8 4.1   4.6   4.7 (a) Find the test statistic. (Give your answer correct to two decimal places.) (ii) Find the p-value. (Give your answer bounds exactly.)  ___< p < ___ (b) State the appropriate conclusion. Reject the null hypothesis, there is not significant evidence of a difference in mean fills. Reject the null hypothesis, there is significant evidence of a difference in mean fills.     Fail to reject the null hypothesis, there is significant evidence of a difference in mean fills. Fail to reject the null hypothesis, there is not significant evidence of a difference in mean fills.

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 + ...