Answered: Data on mean student loans for students…

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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Data on mean student loans for students in a certain area show that the mean student loan total at graduation is $53.5 thousand. Assume a standard deviation of 7.2 thousand.

A. Determine the sampling distribution of the sample mean for samples of size 64

B. Determine the sampling distribution of the sample mean for samples of size 256.

C. Why is it neccessary to assume that the student loan totals are not normally distributed to answer parts (a) and (b)?

D. What is the probability that the sampling error made in estimating the population mean student loan total by the mean loan total of a sample of 64 students will be at most $1000?

E. What is the probability that the sampling error made in estimating the population mean student loan total by the mean loan total of a sample of 256 students will be at most 1000?

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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