Suppose the math department chair at a large state university wants to estimate the average overall rating, out of five points, that students taking Introductory Statistics gave their lecturers on their end-of-term evaluations. She selects a random sample of 38 evaluations and records the summary statistics shown.Sample sizeSample meanSample standard deviationPopulation standard deviationStandard deviation of ?¯Confidence level??⎯⎯⎯????⎯⎯⎯⎯?384.04141.05010.99030.160690%The department chair determines the standard deviation of the sampling distribution of ?⎯⎯⎯ using ?, the standard deviation calculated from all student evaluations submitted to her department. Assume the Statistics lecturers' ratings have the same standard deviation.Use this information to find the margin of error and the lower and upper limits of a 90% confidence interval for ?, the mean overall rating students gave their Introductory Statistics lecturers. Round your answers to the nearest hundredth.

Given Data : Sample Size, n = 38 Sample Mean, x̄ = 4.0414 standard…

Answered: Suppose the math department chair at a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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Suppose the math department chair at a large state university wants to estimate the average overall rating, out of five points, that students taking Introductory Statistics gave their lecturers on their end-of-term evaluations. She selects a random sample of 38 evaluations and records the summary statistics shown.

Sample size	Sample mean	Sample standard deviation	Population standard deviation	Standard deviation of ?¯	Confidence level
?	?⎯⎯⎯	?	?	??⎯⎯⎯⎯	?
38	4.0414	1.0501	0.9903	0.1606	90%

The department chair determines the standard deviation of the sampling distribution of ?⎯⎯⎯ using ?, the standard deviation calculated from all student evaluations submitted to her department. Assume the Statistics lecturers' ratings have the same standard deviation.

Use this information to find the margin of error and the lower and upper limits of a 90% confidence interval for ?, the mean overall rating students gave their Introductory Statistics lecturers. Round your answers to the nearest hundredth.

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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