Answered: An article reported that 8% of married…

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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An article reported that 8% of married couples in the United States are mixed racially or ethnically. Consider the population consisting of all married couples in the United States(a) A random sample of n = 100 couples will be selected from this population and p̂, the proportion of couples that are mixed racially or ethnically, will be computed. 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 it reasonable to assume that the sampling distribution of p̂ is approximately normal for random samples of size n = 100? Explain.

Yes, because np < 10 and n(1 − p) < 10.

Yes, because np > 10 and n(1 − p) > 10.

No, because np < 10.

No, because np > 10.

(c) Suppose that the sample size is n = 250 rather than n = 100, as in Part (b). Does the change in sample size change the mean and standard deviation of the sampling distribution of p̂? What are the values for the mean and standard deviation when n = 250? (Round your standard deviation to four decimal places.)

mean	?
standard deviation	?

(d) Is it reasonable to assume that the sampling distribution of p̂ is approximately normal for random samples of size n = 250? Explain.

Yes, because np < 10.

Yes, because np > 10.

No, because np < 10.

No, because np > 10.

(c) When n = 250, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.1? (Round your answer to four decimal places.)

Answer: ?

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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