The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 8 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. If required, round your answer to three decimal places. (a)Show the sampling distribution of the sample mean annual rainfall for California. E(x)σx̄California (b)Show the sampling distribution of the sample mean annual rainfall for New York. E(x)σx̄New York (c)In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why? The standard error is for New York because the sample size is than for California. The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for bothstates is 8 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. If required, round your answer to three decimalplaces.(a) Show the sampling distribution of the sample mean annual rainfall for California.E(X)California22(b) Show the sampling distribution of the sample mean annual rainfall for New York.E(X)New York42(c) In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why?The standard error is smallerfor New York because the sample size is largerthan for California.

Given,for California:mean=22standard deviation(σ)=8sample size(n)=30for New York :mean=42standard…

Answered: The state of California has a mean…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 8 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. If required, round your answer to three decimal places.

(a)

Show the sampling distribution of the sample mean annual rainfall for California.

	E(x)	σ_x̄
California

(b)

Show the sampling distribution of the sample mean annual rainfall for New York.

	E(x)	σ_x̄
New York

(c)

In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why?

The standard error is for New York because the sample size is than for California.

The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both
states is 8 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. If required, round your answer to three decimal
places.
(a) Show the sampling distribution of the sample mean annual rainfall for California.
E(X)
California
22
(b) Show the sampling distribution of the sample mean annual rainfall for New York.
E(X)
New York
42
(c) In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why?
The standard error is smaller
for New York because the sample size is larger
than for California.

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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