5. To examine the effects of pets and friends in stressful situations, researchers recruited 40 people to participate in an experiment. Subjects were randomly assigned to one of three groups to perform a stressful task alone (control group), with a good friend present, or with their dog present. Each subjects mean heart rate during the task was recorded. Higher heart rates mean more stress. Use an alpha of .05. Control n₁ = 12 M₁ = 85.7 $1 = 3.4 SS = 127.16 SSBetween 263.01 Pets n2 = 14 M₂ = 83.2 S2 = 2.5 SS=81.25 Friends n3 = 14 M3 = 89.3 S3 = 3.5 SS= 159.25 a) What are the hypotheses for this test? b) What is the critical value? c) Complete the necessary calculations (include post hocs if necessary).

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 + ...