Answered: A) If the distribution of sample means…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A) If the distribution of sample means is bell-shaped, how do you decide whether to use a z or t test statistic?

B) When estimating a standard deviation with n = 100, does the population still need to be normally distributed?

C) What happens to the width of the confidence interval if the sample size increases?

Choose One: Increases Decreases Stays the same

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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A) Use of Z-statistic or t-statistic is depends on sample size. If sample size n is large ( >30) then z-statistic is used. If the sample size n is small ( <30) then t-statistic is used. So if the distribution of sample means is bell-shaped, whether to use z-statistic or t-statistic is depends on sample size.

B) Sample Standard deviation is estimated as , S= $\sqrt{\frac{\sum_{i} {(x_{i} - \bar{x})}^{2}}{n - 1}}$

Here $\bar{x}$ is a mean of sample and sample is taken from normally distributed population. also given sample size n is large .

So when estimating a standard deviation with n =100 , population need to be normally distributed.

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