Answered: Suppose that in a large population of…

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

Suppose that in a large population of students, the mean amount of sleep the previous night was ? = 7 hours and the standard deviation was ? = 1.6 hours. Consider randomly selected samples of n = 210 students.

(a) What is the value of the mean of the sampling distribution of possible sample means?
Mean =

(b) Calculate the standard deviation, s.d., of the sampling distribution of possible sample means. (Round your answer to three decimal places.)

s.d.(x)

=

(c) Use the Empirical Rule to find values that fill in the blanks at the end of the following sentence. (Round your answers to three decimal places.)

For 68% of all randomly selected samples of n = 210 students, the mean amount of sleep the previous night will be between and hours.

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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