Answered: A news article estimated that only 4%…

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

100%

A news article estimated that only 4% of those ages 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans ages 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.04.

(a)

A random sample of

n = 100

people will be selected from this population and p̂, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p̂? (Round your standard deviation to four decimal places.)

mean

standard deviation

(b)

Is the sampling distribution of p̂ approximately normal for random samples of size

n = 100?

Explain. (Select all that apply.)

the sampling distribution of p̂ is approximately normal

the sampling distribution of p̂ is not approximately normal

np is less than 10

np equals 10

np is greater than 10

n(1 − p) is less than 10

n(1 − p) equals 10

n(1 − p) is greater than 10

(c)

Suppose that the sample size is

n = 400

rather than

n = 100.

What are the values for the mean and standard deviation when

n = 400?

(Round your standard deviation to four decimal places.)

mean

standard deviation

Does the change in sample size affect the mean and standard deviation of the sampling distribution of p̂? If not, explain why not. (Select all that apply.)

When the sample size increases, the mean increases.When the sample size increases, the mean decreases.When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size.When the sample size increases, the standard deviation increases.When the sample size increases, the standard deviation decreases.When the sample size increases, the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution, regardless of sample size.

(d)

Is the sampling distribution of p̂ approximately normal for random samples of size

n = 400?

Explain. (Select all that apply.)

the sampling distribution of p̂ is approximately normalthe sampling distribution of p̂ is not approximately normalnp is less than 10np equals 10np is greater than 10n(1 − p) is less than 10n(1 − p) equals 10n(1 − p) is greater than 10

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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