Answered: A class survey in a large class for…

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

A class survey in a large class for first‑year college students asked, "About how many hours do you study in a typical week?" The mean response of the 456 students was x¯=17 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation σ=8 hours in the population of all first‑year students at this university.

(a) What is the 99% confidence interval for the population mean? (Enter your answers rounded three decimal places.)

lower bound:

upper bound:

(b) What condition must be met for your confidence interval to be valid?

The confidence interval must contain 0 to satisfy conditions for inference.

The 456 students in this class must be a random sample of all of the first‑year students at this university to satisfy conditions for inference.

The 456 students in this class must be a matched pairs sample of all of the first‑year students at this university to satisfy conditions for inference.

The mean must be greater than 10 to satisfy conditions for inference.

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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