Answered: 7.4 IPHONE APPS The iPhone maker Apple…

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

7.4 IPHONE APPS The iPhone maker Apple announces that 25% of iPhone owners use a certain app. Let
�
be a binary random variable that equals 1 if a randomly selected iPhone owner uses this particular app, and 0 otherwise.

State the population distribution of
�
using the information Apple provides. (That is, give the proportion of times that you expect a randomly selected owner to use or not use the app.)

For a random sample of 50 iPhone owners, 30 use the app. State the data distribution for
�
based on this sample.

Find the mean of the sampling distribution of the sample proportion who use the app in a random sample of 50 owners.

Find the standard deviation of the sampling distribution of the sample proportion who use the app in a random sample of 50 owners.

Explain what the standard deviation in part d describes.

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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