Q 1.37. - Elementary Statistics

Question

The members of a population are numbered 1-4.

(a). List the 6 possible samples (without replacement) of size 2 from this population. 

(b). If an SRS of size 2 is taken from the population, what are the chances of selecting 2 and 3? Explain your answer.

(c). Use Table I in Appendix A to obtain an SRS of size 2 from the population. Start at the single-digit number in line number 17 and column number 7, read down the column, up the next, and so on.

Step-by-Step Solution

Answer

Part (a) 

S.No.	Samples
1	1, 2
2	1, 3
3	1, 4
4	2, 3
5	2,4
6	3, 4

Part (b) 0.167.

Part (c) 1 and 4

Part (a) Step 1. Given information.

The given information is:

The members of a population are numbered 1-4.

It means the population consists of numbers1, 2, 3, and 4.

Part (a) Step 2. List the 6 possible samples (without replacement) of size 2 from this population.

Make a list of the six possible samples for the population without replacing any of them.

As a result, the following are the 6 possible samples for the given population without size 2 replacement: 

S.No.	Samples
1	1, 2
2	1, 3
3	1, 4
4	2, 3
5	2,4
6	3, 4

Part (b) Step 1. Explain if an SRS of size 2 is taken from the population, what are the chances of selecting 2 and 3.

It is evident from section (a) that there are six samples for the specified population. 

Furthermore, each sample has an equal probability of being chosen. 

Also, for numbers 2 and 3, there is only one sample.

The probability of selecting the sample is with 2 and 3 :

$$\begin{gathered} =\frac{1}{6} \\ =0.167 \end{gathered}$$

Therefore, $0.167$are the chances of selecting 2 and 3.

Part (c) Step 1. Use Table I in Appendix A to obtain an SRS of size 2 from the population.

To get an SRS of size 2 from the population, use Table I in Appendix A.

Follow the procedure given below:

Step 1: Make use of Table I. Numbers at random.

Step 2: Select 17 from the Line Number drop-down menu.

Step 3: In Column Number, select 7.

Step 4: In Line 17, begin with a single-digit number.

Step 5: Pick the first number.

Step 6: Don't use the same numbers twice. Also, exclude 0 and numbers greater than 4. 

Step 7. Go down Column 7 and then up Column 8, the following number is 4. 

Output:

SRS

1        4

Therefore, the SRS of size 2 from the population is 1 and 4.