Small_sedan 55 57 57 55 49 Medium Sedan 61 61 56 65 57 64 Large Sedan 70 76 70 72 76 76  Suv 4WD 74 77 65 65 MiniVan 63 60 57 68 62   The table available below shows the costs per mile​ (in cents) for a sample of automobiles. At alphaαequals=0.01​, can you conclude that at least one mean cost per mile is different from the​ others? Let muμSS​, muμMS​, muμLS​, muμSUV and muμMV represent the mean costs per mile for small​ sedans, medium​ sedans, large​ sedans, SUV​ 4WDs, and minivans respectively. What are the hypotheses for this​ test?     A. H0​: muμSSnot equals≠muμMSnot equals≠muμLSnot equals≠muμSUVnot equals≠muμMV Ha​: muμSSequals=muμMSequals=muμLSequals=muμSUVequals=muμMV   B. H0​: muμSSequals=muμMSequals=muμLSequals=muμSUVequals=muμMV Ha​: muμSSnot equals≠muμMSnot equals≠muμLSnot equals≠muμSUVnot equals≠muμMV   C. H0​: Not all the means are equal. Ha​: muμSSequals=muμMSequals=muμLSequals=muμSUVequals=muμMV   D. H0​: muμSSequals=muμMSequals=muμLSequals=muμSUVequals=muμMV Ha​: Not all the means are equal.   What is the test​ statistic?   FSTATequals=Blank ​(Round to two decimal places as​ needed.) What is the​ P-value?   ​P-valueequals=Blank ​(Round to three decimal places as​ needed.) What is the correct​ conclusion?   ▼   Reject Do not reject H0. There ▼   is not is enough evidence to conclude that mean costs per mile vary across the automobile types.

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 + ...