Chapter 1.1, Problem 23E

Exercises 21—24 refer to the population of animals in the following table. The population is divided into four groups: mammals, birds, reptiles, and fish.

Another sample: Draw a simple random sample of two groups of animals from the four groups, and construct a sample of 20 animals by including all the animals in the sampled groups. What kind of sample is this?

To determine

Tofind:The simple random sample of two groups of animal and the type of sample.

Answer to Problem 23E

The simple random sample of two groups of animal is $\left[2,3\right]$ and the type of sample iscluster.

Explanation of Solution

Given information:The population is divided into four groups: mammals, birds, reptiles, and fish. Refer to the population of animals in the following table.

Mammals	Birds	Reptiles	Fish
Aardvark Buffalo Elephant Squirrel Rabbit Lion Zebra Pig Dog Horse	11. Flamingo 12. Swan 13. Sparrow 14. Parrot 15. Pelican 16. Hawk 17. Owl 18. Chicken 19. Duck 20. Turkey	21. Gecko 22. Iguana 23. Chameleon 24. Rattlesnake 25. Boa constrictor 26. Python 27. Turtle 28. Tortoise 29. Alligator 30. Crocodile	31. Catfish 32. Tuna 33. Cod 34. Salmon 35. Goldfish 36. Shark 37. Trout 38. Perch 39. Guppy 40. Minnow

Concept Involved:

If a sample is taken from a population and each item is equally like to make the sample then the sample is called simple random sample.

Calculation:

Since, the items are drawn from the population in groups, or clusters.

Thus, the type of sample is cluster sample.

Consider a simple random sample of two groups of animals from the four groups, and construct a sample of 20 animals by including all the animals in the sampled groups.

	Group	Samples
Mammals	1	Aardvark, Buffalo, Elephant, Squirrel, Rabbit, Lion, Zebra, Pig, Dog, Horse
Birds	2	Flamingo, Swan, Sparrow, Parrot, Pelican, Hawk, Owl, Chicken, Duck, Turkey
Reptiles	3	Gecko, Iguana, Chameleon, Rattlesnake, Boa constrictor, Python, Turtle, Tortoise, Alligator, Crocodile
Fish	4	Catfish, Tuna, Cod, Salmon, Goldfish, Shark, Trout, Perch, Guppy, Minnow

The step-by-step procedure is shown below.

Step 1: Enter any nonzero number on the HOME screen as the seed Step 2: Press $STO>$ Step 3: Press $MATH$, select $PRB$, then $1:rand$, and then press $ENTER$. This enters the seed into the calculator memory. See Figure A. which uses the number 2 as the seed. Step 4: Press $MATH$, select $PRB$, then $5:randInt.$ Then enter $1,N,n$ where $N$ is total number of groups and $n$ is the desired sample of clusters. Here we use $N=4$ and $n=2$ (Figure B). Step 5: Press $ENTER$ . The two values in the random sample of groups, here we get $3,2$ (Figure C).

$\begin{array}{l}\boxed{\begin{array}{l}2\to rand\\ \\ \\ \end{array}}\\ FigureA\end{array}$$\begin{array}{l}\boxed{\begin{array}{l}randInt\left(1,4,2\right)\\ \\ \\ \end{array}}\\ FigureB\end{array}$$\begin{array}{l}\boxed{\begin{array}{l}randInt\left(1,4,2\right)\\ \left(32\right)\\ \\ \\ \end{array}}\\ FigureC\end{array}$

Therefore, the simple random sample of two groups of animal is $\left[2,3\right]$ and the type of sample iscluster.