1. This question will use Excel to select random samples of varying sizes from a uniformdistribution on the interval 1 to 10. The goal is to demonstrate the effect of sample sizeon 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 ribbonyou 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, andthen in the Manage box, select Excel Add-ins. Click Go. Select Analysis ToolPakand click Ok.(c) You should now see the Data Analysis dialog box Select Random Number Generationand 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 asthe random samples drawn from the uniform distribution on 1-10. In this casethis means that there are 50 samples each of size 2. In the first cell of the emptycolumn (cell C1 for this case) enter a formula to find the mean of your sample inthe first row. Drag the formula down to the end of the data, i.e. to row 50. The50 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 standarddeviation of this sample. Create a histogram of the distribution of the sample ofmeans. For the histogram use boundaries 1, 2, 3 ...10. Refer to Assignment 1 fordirections 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 distributionof means, lz, equals the population mean and the standard deviation of the meansequals the population standard deviation divided by the square root of the samplesize, o7 =How do your numbers compare to the theoretical values? Answer this question bycompleting the table below as it relates to your samples. Use 3 decimal places.Sample Size Observed ValuesTheoretical ValuesMeanStandard Deviation2(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, thecompleted table from part (g) and the answer to (h).

Question

Accepted Answer

“Since you have posted a question with multiple sub-parts, we will solve first three subparts for…