Answered: Virginia 30083, 32159, 31009, 34384,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

In a current study, a random sample of 10 teachers from Texas and an independent random sample of 10 teachers from Virginia have been asked to report their annual income. The data obtained are as follows. (See attachment for data table and full question).

The population standard deviations for the annual incomes of teachers in Texas and in Virginia are estimated as $6100 and $6600, respectively. It is also known that both populations are approximately normally distributed. Construct a 95% confidence interval for the difference −μ1μ2 between the mean annual income of teachers from Texas (μ1) and the mean annual income of teachers from Virginia (μ2). Then find the lower limit and upper limit of the 95% confidence interval.

Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places.

a.) The Lower Limit is:

b.) The Upper Limit is:

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In a current study, a random sample of 10 teachers from Texas and an independent random sample of 10 teachers from
Virginia have been asked to report their annual income. The data obtained are as follows.
Annual income in dollars
Texas 39907, 23242, 36328, 34628, 42540, 44708, 34717, 45291, 27064, 31139
Virginia 30083, 32159, 31009, 34384, 38196, 35798, 43330, 26261, 44537, 35679
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The population standard deviations for the annual incomes of teachers in Texas and in Virginia are estimated as $6100
and $6600, respectively. It is also known that both populations are approximately normally distributed. Construct a 95%
confidence interval for the difference μ₁-₂ between the mean annual income of teachers from Texas (μ₁) and the mean
annual income of teachers from Virginia (μ₂). Then find the lower limit and upper limit of the 95% confidence interval.
Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal
places. (If necessary, consult a list of formulas.)
Lower limit:
Upper limit:
X
Ś
0

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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