Defining Parameters Accurately: Difference of Two Means

In a random sample of 25 males in the U.S., the mean weight is 170 pounds, with a standard deviation of 20 pounds. In an independent random sample of 36 females in the U.S., the mean weight is 130 pounds, with a standard deviation of 15 pounds. We want to know how much taller guys are, on average, than gals are.

Which of the following is the most accurate way to describe the parameter of interest?

Group of answer choices

( ) Define:

mu_1 = the mean weight of all males in the U.S.

mu_2 = the mean weight of all females in the U.S.

We are interested in mu_1 - mu_2.

( ) Define:

mu_1 = the mean for males.

mu_2 = the mean for females.

We are interested in mu_1 - mu_2.

( ) mu_1 = all males in the U.S.

mu_2 = all females in the U.S.

We are interested in mu_1 - mu_2.

( )Define:

mu_1 = the mean weight of the 25 males in the sample.

mu_2 = the mean weight of the 36 females in the sample.

We are interested in mu_1 - mu_2.

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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