Answered: A government sample survey plans to…

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 government sample survey plans to measure the LDL (bad) cholesterol level of an SRS of men aged 20 to 34.
Suppose that in fact the LDL cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean

μ = 115

milligrams per deciliter (mg/dL) and standard deviation

σ = 25 mg/dL.

Use Table A for the following questions, where necessary.

(a) Choose an SRS of 100 men from this population. What is the sampling distribution of x? (Use the units of mg/dL.)

N(115, 2.5)N(115, 25) N(0.115, 0.025)N(115, 0.25)N(1.15, 0.25)

What is the probability that x takes a value between 113 and 117 mg/dL? This is the probability that x estimates μ within ±2 mg/dL. (Round your answer to three decimal places.)

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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