13. For the following studies, determine the null and alternative hypotheses and classify thehypothesis test as two tailed, left-tailed or right-tailed.a) A study was conducted comparing the wing lengths of two subspecies of dark-eyedjuncos. One of the subspecies migrates, the other does not. A hypothesis test is to beperformed to decide whether the mean wing length of the non-migratory birds is lessthan that of the migratory birds.b) A half-century ago, the average (U.S.) woman in her 20s was 62.6 inches tall. To see ifwoman tend to be taller, a random sample of 1000 women in their 20s was recentlyconducted and heights were recorded. A hypothesis test is to be performed to decide ifthe mean height of women in their 20s today is greater than that of the women in their20s a half-century ago.

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 + ...

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