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1. This question will use Excel to select random samples of varying sizes from a uniform distribution on the interval 1 to 10. The goal is to demonstrate the effect of sample size on the shape of the sampling distribution of the mean. (a) Open the Excel and go to the DATA tab. (b) Select Data Analysis on the ribbon. If Data Analysis is not available on the ribbon you must install the Analysis Toolpak add-in (see Sakai-Resources-Excel). * Load the Data Analysis ToolPak: Click the File tab, and then click Options. Select Add-Ins on the left, click Analysis ToolPak in the list on the right, and then in the Manage box, select Excel Add-ins. Click Go. Select Analysis ToolPak and click Ok. (c) You should now see the Data Analysis dialog box Select Random Number Generation and click OK. * for Number of Variables enter 2 * for Number of Random Numbers enter 50 * for Distribution select Uniform * for Parameters enter Between 1 and 10 * for Output options Select New Worksheet Ply * You will see 50 rows and the random samples drawn from the uniform distribution on 1-10. In this case this means that there are 50 samples each of size 2. In the first cell of the empty column (cell C1 for this case) enter a formula to find the mean of your sample in the first row. Drag the formula down to the end of the data, i.e. to row 50. The 50 means in column C1 become out first sample of means. columns of numbers. The rows will be considered as (d) Copy your means to a new worksheet. Use Excel to calculate the mean and standard deviation of this sample. Create a histogram of the distribution of the sample of means. For the histogram use boundaries 1, 2, 3 ...10. Refer to Assignment 1 for directions on histograms (e) Repeat Steps (c) and (d) three more times

1. This question will use Excel to select random samples of varying sizes from a uniform distribution on the interval 1 to 10. The goal is to demonstrate the effect of sample size on the shape of the sampling distribution of the mean. (a) Open the Excel and go to the DATA tab. (b) Select Data Analysis on the ribbon. If Data Analysis is not available on the ribbon you must install the Analysis Toolpak add-in (see Sakai-Resources-Excel). * Load the Data Analysis ToolPak: Click the File tab, and then click Options. Select Add-Ins on the left, click Analysis ToolPak in the list on the right, and then in the Manage box, select Excel Add-ins. Click Go. Select Analysis ToolPak and click Ok. (c) You should now see the Data Analysis dialog box Select Random Number Generation and click OK. * for Number of Variables enter 2 * for Number of Random Numbers enter 50 * for Distribution select Uniform * for Parameters enter Between 1 and 10 * for Output options Select New Worksheet Ply * You will see 50 rows and the random samples drawn from the uniform distribution on 1-10. In this case this means that there are 50 samples each of size 2. In the first cell of the empty column (cell C1 for this case) enter a formula to find the mean of your sample in the first row. Drag the formula down to the end of the data, i.e. to row 50. The 50 means in column C1 become out first sample of means. columns of numbers. The rows will be considered as (d) Copy your means to a new worksheet. Use Excel to calculate the mean and standard deviation of this sample. Create a histogram of the distribution of the sample of means. For the histogram use boundaries 1, 2, 3 ...10. Refer to Assignment 1 for directions on histograms (e) Repeat Steps (c) and (d) three more times

MATLAB: An Introduction with Applications
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. This question will use Excel to select random samples of varying sizes from a uniform distribution on the interval 1 to 10. The goal is to demonstrate the effect of sample size on the shape of the sampling distribution of the mean. (a) Open the Excel and go to the DATA tab. (b) Select Data Analysis on the ribbon. If Data Analysis is not available on the ribbon you must install the Analysis Toolpak add-in (see Sakai-Resources-Excel). * Load the Data Analysis ToolPak: Click the File tab, and then click Options. Select Add-Ins on the left, click Analysis ToolPak in the list on the right, and then in the Manage box, select Excel Add-ins. Click Go. Select Analysis ToolPak and click Ok. (c) You should now see the Data Analysis dialog box Select Random Number Generation and click OK. * for Number of Variables enter 2 * for Number of Random Numbers enter 50 * for Distribution select Uniform * for Parameters enter Between 1 and 10 * for Output options Select New Worksheet Ply * You will see 50 rows and 2 columns of numbers. The rows will be considered as the random samples drawn from the uniform distribution on 1-10. In this case this means that there are 50 samples each of size 2. In the first cell of the empty column (cell C1 for this case) enter a formula to find the mean of your sample in the first row. Drag the formula down to the end of the data, i.e. to row 50. The 50 means in column C1 become out first sample of means. (d) Copy your means to a new worksheet. Use Excel to calculate the mean and standard deviation of this sample. Create a histogram of the distribution of the sample of means. For the histogram use boundaries 1, 2, 3 ...10. Refer to Assignment 1 for directions on histograms (e) Repeat Steps (c) and (d) three more times
Transcribed Image Text:1. This question will use Excel to select random samples of varying sizes from a uniform distribution on the interval 1 to 10. The goal is to demonstrate the effect of sample size on the shape of the sampling distribution of the mean. (a) Open the Excel and go to the DATA tab. (b) Select Data Analysis on the ribbon. If Data Analysis is not available on the ribbon you must install the Analysis Toolpak add-in (see Sakai-Resources-Excel). * Load the Data Analysis ToolPak: Click the File tab, and then click Options. Select Add-Ins on the left, click Analysis ToolPak in the list on the right, and then in the Manage box, select Excel Add-ins. Click Go. Select Analysis ToolPak and click Ok. (c) You should now see the Data Analysis dialog box Select Random Number Generation and click OK. * for Number of Variables enter 2 * for Number of Random Numbers enter 50 * for Distribution select Uniform * for Parameters enter Between 1 and 10 * for Output options Select New Worksheet Ply * You will see 50 rows and 2 columns of numbers. The rows will be considered as the random samples drawn from the uniform distribution on 1-10. In this case this means that there are 50 samples each of size 2. In the first cell of the empty column (cell C1 for this case) enter a formula to find the mean of your sample in the first row. Drag the formula down to the end of the data, i.e. to row 50. The 50 means in column C1 become out first sample of means. (d) Copy your means to a new worksheet. Use Excel to calculate the mean and standard deviation of this sample. Create a histogram of the distribution of the sample of means. For the histogram use boundaries 1, 2, 3 ...10. Refer to Assignment 1 for directions on histograms (e) Repeat Steps (c) and (d) three more times
* The second time set the Number of Variables to any a value between 5 and 10 * The third time set the Number of Variables to any a value between 20 and 25 * The fourth time set the Number of Variables to any a value between 31 and 36 (f) You have a total of 4 samples of means and a histogram of each. Arrange the his- tograms so they are all on one page. (g) For the uniform distribution on 1 to 10 the population mean is 5.5 and the popula- tion standard deviation is 2.5981. In theory the mean of the sampling distribution of means, lz, equals the population mean and the standard deviation of the means equals the population standard deviation divided by the square root of the sample size, o7 = How do your numbers compare to the theoretical values? Answer this question by completing the table below as it relates to your samples. Use 3 decimal places. Sample Size Observed Values Theoretical Values Mean Standard Deviation 2 (h) How does the distribution of means change as n increases i.e.: * How do the values of the means change? * How do the values of the standard deviation change? * is the shape of the distribution becoming more normal? Note: The answer to this question will consist of screenshots of the 4 histograms, the completed table from part (g) and the answer to (h).
Transcribed Image Text:* The second time set the Number of Variables to any a value between 5 and 10 * The third time set the Number of Variables to any a value between 20 and 25 * The fourth time set the Number of Variables to any a value between 31 and 36 (f) You have a total of 4 samples of means and a histogram of each. Arrange the his- tograms so they are all on one page. (g) For the uniform distribution on 1 to 10 the population mean is 5.5 and the popula- tion standard deviation is 2.5981. In theory the mean of the sampling distribution of means, lz, equals the population mean and the standard deviation of the means equals the population standard deviation divided by the square root of the sample size, o7 = How do your numbers compare to the theoretical values? Answer this question by completing the table below as it relates to your samples. Use 3 decimal places. Sample Size Observed Values Theoretical Values Mean Standard Deviation 2 (h) How does the distribution of means change as n increases i.e.: * How do the values of the means change? * How do the values of the standard deviation change? * is the shape of the distribution becoming more normal? Note: The answer to this question will consist of screenshots of the 4 histograms, the completed table from part (g) and the answer to (h).
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