Question

Element Hunters. In the article "Element Hunters" (National Geographic, Vol. 233, No. 5, pp. 112-120), R. Dunn reports about the search for new undiscovered elements. Since 1940, scientists have been synthesizing elements one by one. The first was neptunium (Np), element number 93. There are, as of this writing, a total of 26 new synthetic elements. The following table provides their element numbers and symbols.

(a) Suppose that you decide to take a simple random sample of eight of these new elements. Use Table I in Appendix A to obtain eight random numbers that you can use to specify your sample.

(b) If you have access to a random-number generator, use it to solve part (a).

Short answer

Part (a) Np, Am, Fm, Lr, Ds, FI, Bh, and Rg.

Part (b) Fm, Hs, Cm, Lr, Bh, Es, Fl, and Uus.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

There are a total of 26 new synthetic elements. Firstly we will assign each element a number:

S. No.	Number	Symbol	S. No.	Number	Symbol
1	93	Np	14	106	Sg
2	94	Pu	15	107	Bh
3	95	Am	16	108	Hs
4	96	Cm	17	109	Mt
5	97	Bk	18	110	Ds
6	98	Cf	19	111	Rg
7	99	Es	20	112	Cn
8	100	Fm	21	113	Uut
9	101	Md	22	114	Fl
10	102	No	23	115	Uup
11	103	Lr	24	116	Lv
12	104	Rf	25	117	Uus
13	105	Db	26	118	Uuo

Part (a) Step 2. Obtain a random sample of size 8 by using Table I in Appendix A.

To make an example, use Table I in Appendix A to create an SRS of size 8.

Follow the below-given procedure:

Step 1: Look up random numbers in Table I.

Step 2: Select 10 as the line number.

Step 3: Select Columns 10 and 11.

Step 4: In Line 10-11, begin using two-digit numerals.

Step 5: Pick the first number, which is 01.

Step 6: Avoid digits 27 to 99 and avoid repetition of numerals.

Step 7: Continue up the 12-13 column to get the second number, which is 03.

Step 8: Move up the column to the third number, which is 08

Step 9: Go along the column to the fourth number, which is 11.

Step 10: Go along the column to the fifth number, which is 18.

Step 11: Continue down the column 14-15 until you reach the sixth number, which is 22.

Step 12: Go down the column to the seventh number, which is 15.

Step 13: Count up from 16 to 17 in the column to get the eighth number, which is 19.

Output:

1, 3, 8, 11, 18, 22, 15, 19

The resultant new elements that make up a size 8 SRS are Np, Am, Fm, Lr, Ds, FI, Bh, and Rg.

Part (b) Step 1. Use a random number generator to solve part (a).

To get an SRS of size 8 from the population, use MINITAB.

Follow the below-given procedure for MINITAB:

Step 1: Select Calc > Random Data > Integer from the menu bar.

Step 2: Double your selected sample size in the Number of rows of data to generate a section, just in case there are repeats. Set the sample size to eight.

Step 3: In the Store in a column, type SRS in column C1.

Step 4: Enter 01 as the minimum value.

Step 5: Enter 26 as the maximum value.

Step 6: Click the OK button.

MINITAB output is:

13, 16, 4, 11, 15, 7, 22, 25

Therefore, the sample includes Fm, Hs, Cm, Lr, Bh, Es, Fl, and Uus.