3. 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. This problem is similar to Example 1 page 308 of the text.
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 as described on page 42 of the text.
C. You should now see the Data Analysis dialog box Select Random Number Generation and click
OK. (See diagram page 525 of the text.)
? 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 second time set the Number of Variables to any a value between 20 and 25
? The second 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 histograms so they are all on one page.
G. For the uniform distribution on 1 to 10 the population mean is 5.5 and the population standard deviation is 2.5981. In ,