Question 4.7

4.7 Random digits.

As discussed in Chapter 3, generation of random numbers is one approach for obtaining a simple random sample (SRS). If we were to look at the random generation of digits, the mechanism should give each digit probability 0.1. Consider the digit “0” in particular.

  1. The table of random digits (Table B) was produced by a random mechanism that gives each digit probability 0.1 of being a 0. What proportion of the first 200 digits in the table are 0s? This proportion is an estimate, based on 200 repetitions, of the true probability, which in this case is known to be 0.1.
  2. Now use software assigned by your instructor:
    • Excel users: Enter the formula RANDBETWEEN(0,9) in cell A1. Now, drag and copy the contents of cell A1 into cells A2:A1000. You will find 1000 random digits appear. Any attempt to copy these digits for sorting purposes will result in the digits changing. You will need to “freeze” the generated values. To do so, highlight column 1 and copy the contents and then Paste Special as Values the contents into the same or any other column. The values will now not change. Finally, use Excel to sort the values in ascending order.
    • JMP users: With a new data table, right-click on the header of Column 1 and choose Column Info. In the drag-down dialog box named Initialize Data, pick Random option. Choose the bullet option of Random Integer, and set Minimum/Maximum to 0 and 9. Input the value of 1000 into the Number of rows box, and then click OK. The values can then be sorted in ascending order using the Sort option found under Tables.
    • Minitab users: Do the following pull-down sequence: Calc→ Random Data→ Integer. Enter “1000” in the Number of rows of data to generate box, type “c1” in the Store in column(s) box, enter “0” in the Minimum value box, and enter “9” in the Maximum box. Click OK to find 1000 realizations of outputted in the worksheet. The values can then be sorted in ascending order using the Sort option found under Data.

Based on the software you used, what proportion of the 1000 randomly generated digits are 0s? Is this proportion close to 0.1?

4.7

(a) 0.105. (b) Answers should be close to 0.1.