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.a)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. b) 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) The image illustrates a concept related to statistical confidence intervals and confidence levels.At the top, there is a bell-shaped curve, representing a normal distribution. - On either side of the curve, there are labeled sections with "α/2 = ___," indicating the tails of the distribution. The α (alpha) level represents the significance level in hypothesis testing, and dividing by 2 indicates that the area is split between the two tails for a two-tailed test. - In the center, the peak of the curve is labeled "C.L. = ___," which stands for Confidence Level. This indicates the percentage of the area under the curve that falls within the confidence interval, typically expressed as a percentage (e.g., 95%). - Parallel lines below the curve are pointing inward from the extremes towards the center are likely representing the range of the confidence interval.- The letter "p'" appears at the bottom right, which might signify a sample proportion or point estimate.The diagram visually conveys how a confidence interval encompasses the central region of a probability distribution curve, with the confidence level determining its width and the alpha level indicating the remaining probability split in the tails.

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

Answered: Announcements for 83 upcoming…

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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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.

a)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.

b) 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)

The image illustrates a concept related to statistical confidence intervals and confidence levels.

At the top, there is a bell-shaped curve, representing a normal distribution.

- On either side of the curve, there are labeled sections with "α/2 = ___," indicating the tails of the distribution. The α (alpha) level represents the significance level in hypothesis testing, and dividing by 2 indicates that the area is split between the two tails for a two-tailed test.

- In the center, the peak of the curve is labeled "C.L. = ___," which stands for Confidence Level. This indicates the percentage of the area under the curve that falls within the confidence interval, typically expressed as a percentage (e.g., 95%).

- Parallel lines below the curve are pointing inward from the extremes towards the center are likely representing the range of the confidence interval.

- The letter "p'" appears at the bottom right, which might signify a sample proportion or point estimate.

The diagram visually conveys how a confidence interval encompasses the central region of a probability distribution curve, with the confidence level determining its width and the alpha level indicating the remaining probability split in the tails.

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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