Announcements for 83 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.96 days, with a standard deviation of 1.24 days. Assume the underlying population is normal. 1)In words define the random variables x and x̅ X is the mean length from a sample of 83 engineering conferences and x̅ is the length of an engineering conference. X is the length of an engineering conference and x̅ is the mean length from a sample of 83 engineering conferences.X is the number of engineering conferences and x̅ is the mean number of engineering conferences listed in IEEE spectrum magazine.X is the mean number of engineering conferences listed in IEEE spectrum magazine and x̅ is the number of engineering conferences. 2)Which distribution should you use for this problem? Explain your choice.The student’s t-distribution should be used because the sample mean is smaller than 30. The student’s t-distribution should be used because the sample standard deviation is given. The standard normal distribution should be used because the mean is given. The standard normal distribution should be used because the population standard deviation is known. 3) Construct a 95% confidence interval for the population mean length of engineering conferences. (I)State the confidence interval. (round your answers two decimal points.)(__________ , ___________)(ii)Sketch the graph (round your answers to two decimal places. Enter your a/2 to three decimal places.)(iii)Calculate the error bound. (round your answers two decimal points.)for the image its for part 3 (ii) aC.L. =2%3DP'

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Description: Announcements for 83 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.96 days, with a standard deviation of 1.24 days. Assume the underlying population is normal.

Let X denoted the length of engineering conference and X¯ denotes the mean length of 83 engineering…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Announcements for 83 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.96 days, with a standard deviation of 1.24 days. Assume the underlying population is normal.

1)In words define the random variables x and x̅

X is the mean length from a sample of 83 engineering conferences and x̅ is the length of an engineering conference.
X is the length of an engineering conference and x̅ is the mean length from a sample of 83 engineering conferences.
X is the number of engineering conferences and x̅ is the mean number of engineering conferences listed in IEEE spectrum magazine.
X is the mean number of engineering conferences listed in IEEE spectrum magazine and x̅ is the number of engineering conferences.

2)Which distribution should you use for this problem? Explain your choice.

The student’s t-distribution should be used because the sample mean is smaller than 30.
The student’s t-distribution should be used because the sample standard deviation is given.
The standard normal distribution should be used because the mean is given.
The standard normal distribution should be used because the population standard deviation is known.

3) Construct a 95% confidence interval for the population mean length of engineering conferences.

(I)State the confidence interval. (round your answers two decimal points.)

(__________ , ___________)

(ii)Sketch the graph (round your answers to two decimal places. Enter your a/2 to three decimal places.)

(iii)Calculate the error bound. (round your answers two decimal points.)

for the image its for part 3 (ii)

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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