Answered: True or false? The value zc is a value…

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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1. True or false? The value z_c is a value from the standard normal distribution such that P(−z_c < z < z_c) = c.

True. By definition, critical values z_c are such that 100c% of the area under the standard normal curve falls in the tails, to the left of −z_c and to the right of z_c.

False. By definition, critical values z_c are such that 100c% of the area under the standard normal curve falls between −z_c and z_c.

True. By definition, critical values z_c are such that 100c% of the area under the standard normal curve falls between −z_c and z_c.

False. By definition, critical values z_c are such that 100c% of the area under the standard normal curve falls in the tails, to the left of −z_c and to the right of z_c.

2. True or false? The point estimate for the population mean μ of an x distribution is , computed from a random sample of the x distribution.

True. The mean of the distribution equals the mean of the x distribution and the standard error of the distribution decreases as n increases.

False. The mean of the distribution does not equal the mean of the x distribution and the standard error of the distribution decreases as n increases.

True. The mean of the distribution equals the mean of the x distribution and the standard error of the distribution increases as n increases.

False. The mean of the distribution does not equal the mean of the x distribution and the standard error of the distribution increases as n increases.

3. Sam computed a 90% confidence interval for μ from a specific random sample of size n. He claims that at the 90% confidence level, his confidence interval contains μ. Is this claim correct? Explain.

Yes. 90% of all confidence intervals will contain μ.

No. The probability that this interval contains μ is either 0 or 1.

No. The proportion of all confidence intervals based on random samples of size n that contain μ is 0.10.

Yes. The proportion of all confidence intervals based on random samples of size n that contain μ is 0.90.

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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