The following data were collected in an experiment designed to investigate the impact of different positions of the mother on fetal heart rate. Fetal heart rate is measured by ultrasound in beats per minute. The study included 20 women who were assigned to one position and had the fetal heart rate measured in that position. Each woman was between 28-32 weeks gestation. The data are shown below. Back Side Sitting Standing 140 141 144 147 144 143 145 145 146 145 147 148 141 144 148 149 139 136 144 145 Is there a significant difference in mean fetal heart rates by position? Run the test at a 5% level of significance. Write out the appropriate null hypothesis and the alternative hypothesis   calculate and report the appropriate test statistic. Please show your work.   decide to either fail to reject null hypothesis or reject null hypothesis in favor of the alternative hypothesis and describe the result and the statistical conclusion in an understandable way.

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 + ...