Assume you have a population which has been measured on a scale of career ambition with p = 150 and 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 the mean in this sample. Then you have replaced the individuals in the population and have drawn another sample of size 100. You keep doing this repeatedly until you have a list of the sample means in a huge number of samples from this population. Now you make a plot of the means of all the samples (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 population mean? 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 the standard 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 the relationship of the standard error of the mean to the standard deviation of the raw scores. 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 off three 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 population distribution of career ambition scores from which the samples are taken is not normally distributed, but rather is somewhat skewed. a. What does the central limit theorem state? Under what circumstances do we need the central limit theorem? b. What will be the shape of the distribution of means in this example?
Assume you have a population which has been measured on a scale of career ambition with p = 150 and 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 the mean in this sample. Then you have replaced the individuals in the population and have drawn another sample of size 100. You keep doing this repeatedly until you have a list of the sample means in a huge number of samples from this population. Now you make a plot of the means of all the samples (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 population mean? 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 the standard 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 the relationship of the standard error of the mean to the standard deviation of the raw scores. 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 off three 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 population distribution of career ambition scores from which the samples are taken is not normally distributed, but rather is somewhat skewed. a. What does the central limit theorem state? Under what circumstances do we need the central limit theorem? b. What will be the shape of the distribution of means in this example?
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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please just do 6 and 7. thank you!
Transcribed Image Text:PART I. SAMPLING DISTRIBUTION OF THE MEAN
Assume you have a population which has been measured on a scale of career ambition with u = 150
and 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 the
mean in this sample. Then you have replaced the individuals in the population and have drawn
another sample of size 100. You keep doing this repeatedly until you have a list of the sample means
in a huge number of samples from this population. Now you make a plot of the means of all the
samples (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 population
mean?
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 the
standard 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 the
relationship of the standard error of the mean to the standard deviation of the raw
scores.
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 off
three 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 population
distribution of career ambition scores from which the samples are taken is not normally
distributed, but rather is somewhat skewed.
a. What does the central limit theorem state? Under what circumstances do we need the
central limit theorem?
b. What will be the shape of the distribution of means in this example?
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