Suppose we are about to draw a sample from a normally distributed population, and find a confidence interval for the population mean. Which one of the following statements is true? Question 23 options: If we use a z value when calculating the interval, when we should be using t, the resulting interval will be wider than it should be. If the sample size is large (n > 30, say), we should always use the z method rather than the t approach. All else being equal, the larger the sample size the larger the margin of error. 95% of the observations in the sample will fall within the 95% confidence interval we calculate. A 95% confidence interval will be wider than the corresponding 90% interval calculated on the same data.

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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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Suppose we are about to draw a sample from a normally distributed population, and find a confidence interval for the population mean. Which one of the following statements is true?

Question 23 options:

	If we use a z value when calculating the interval, when we should be using t, the resulting interval will be wider than it should be.
	If the sample size is large (n > 30, say), we should always use the z method rather than the t approach.
	All else being equal, the larger the sample size the larger the margin of error.
	95% of the observations in the sample will fall within the 95% confidence interval we calculate.
	A 95% confidence interval will be wider than the corresponding 90% interval calculated on the same data.

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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