Answered: A manufacturer claims that only 2% 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

A manufacturer claims that only 2% of their products are defective. A store receives a delivery of 300 items from the manufacturer. Let p-hat = the proportion of defective items in a sample of 300 items. Assuming the manufacturer is correct that only 2% of their products are defective, what are the mean and standard deviation of the sampling distribution of p-hat ?

Options:

The mean is 0.02 and the standard deviation is 0.008.

The mean is 6 and the standard deviation is 2.42.

The mean is 6 and the standard deviation is 5.88.

The mean is 0.02 and the standard deviation is 0.196.

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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