PART I. SAMPLING DISTRIBUTION OF THE MEANAssume you have a population which has been measured on a scale of career ambition with u = 150and o = 40. Assume that the ambition scores are normally distributed in the population.Assume that you have drawn a sample of 100 individuals from the population and have recorded themean in this sample. Then you have replaced the individuals in the population and have drawnanother sample of size 100. You keep doing this repeatedly until you have a list of the sample meansin a huge number of samples from this population. Now you make a plot of the means of all thesamples (i.e., you form a distribution of the sample means).1. What is this distribution called?2. What is the numerical value of the mean of the distribution you have created?3. In general, how does the mean of the distribution you have created relate to the populationmean?4. What will be the shape of the distribution of means? Explain your answer.5. Now suppose you calculate the standard deviation of the sample means. Note that thestandard deviation of the sample means is called the standard error of the mean.a. What is the symbol for the standard error of the mean?b. Give the algebraic formula for the standard error of the mean that shows therelationship of the standard error of the mean to the standard deviation of the rawscores.c. What is the value of the standard error of the means for samples of size n = 100?6. Make a sketch of the sampling distribution of the means for samples of size 100, marking offthree standard errors (values from 5c above) on either side of the mean.7. Suppose you were to repeat the whole exercise, but now you were told that the populationdistribution of career ambition scores from which the samples are taken is not normallydistributed, but rather is somewhat skewed.a. What does the central limit theorem state? Under what circumstances do we need thecentral limit theorem?b. What will be the shape of the distribution of means in this example?

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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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ŷ = 0.524(2.645)x ŷ = 2.645(0.524)x ŷ = 2.645x + 0.524 ŷ = 0.524x + 2.645
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