SAMPLING DISTRIBUTIONS AND THE CENTRAL LIMIT THEOREM 273 EXTENDING CONCEPTS ice of gasoline om sample of obability that 1 that week? inistration) Finite Correction Factor The formula for the standard deviation of the sampling distribution of sample means %3D Vn e of gasoline gas stations 1 the mean ? Assume given in the Central Limit Theorem is based on an assumption that the population has infinitely many members. This is the case whenever sampling is done with replacement (each member is put back after it is selected), because the sampling process couta be continued indefinitely, The formula is also valid when the sample size is small tn comparison with the population, When sampling is done without replacement and he sample size n is more than 5% of the finite population of size N (n/ N> 0.05), however, there is a finite number of possible samples. A finite correction factor, ates (ages e group is sample is National VN - 1 should be used to adjust the standard deviation. The sampling distribution of the sample means will be normal with a mean equal to the population mean, and the standard deviation will be es 20-29) selected. greater enter for In Exercises 39 and 40, determine whether the finite correction factor should be used. If so, use it in your calculations when you find the probability. %3D Vn V N - 1 39. Gas Prices In a sample of 900 gas stations, the mean price of regular gasoline at the pump was $3.746 per gallon and the standard deviation was $0.009 per gallon. A random sample of size 55 is selected from this population. What is the probability that the mean price per gallon is less than $3.742? (Adapted from U.S. Department of Energy) 31 are n with ple of 2 are ith a In a sample of 500 eruptions of the Old Faithful geyser men Old Faithful

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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In a sample of 900 gas stations, the mean price of regular gasoline at the pump was $3.746 per gallon and the sta dar deviation was $0.009 per gallon. A random sample of size 55 is selected from this population. What is the probability that the mean price per gallon is less then $3.742?

SAMPLING DISTRIBUTIONS AND THE CENTRAL LIMIT THEOREM
273
EXTENDING CONCEPTS
ice of gasoline
om sample of
obability that
1 that week?
inistration)
Finite Correction Factor The formula for the standard deviation of the
sampling distribution of sample means
%3D
Vn
e of gasoline
gas stations
1 the mean
? Assume
given in the Central Limit Theorem is based on an assumption that the population has
infinitely many members. This is the case whenever sampling is done with replacement
(each member is put back after it is selected), because the sampling process couta
be continued indefinitely, The formula is also valid when the sample size is small tn
comparison with the population, When sampling is done without replacement and
he sample size n is more than 5% of the finite population of size N (n/ N> 0.05),
however, there is a finite number of possible samples. A finite correction factor,
ates (ages
e group is
sample is
National
VN - 1
should be used to adjust the standard deviation. The sampling distribution of the
sample means will be normal with a mean equal to the population mean, and the
standard deviation will be
es 20-29)
selected.
greater
enter for
In Exercises 39 and 40, determine whether the finite correction factor should be
used. If so, use it in your calculations when you find the probability.
%3D
Vn V N - 1
39. Gas Prices In a sample of 900 gas stations, the mean price of regular
gasoline at the pump was $3.746 per gallon and the standard deviation
was $0.009 per gallon. A random sample of size 55 is selected from this
population. What is the probability that the mean price per gallon is less
than $3.742? (Adapted from U.S. Department of Energy)
31 are
n with
ple of
2 are
ith a
In a sample of 500 eruptions of the Old Faithful geyser
men
Old Faithful

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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