Question

A real estate company manages apartment complexes in a certain city. They currently have 30 units available for rent. The monthly rental prices​ (in dollars) for this population of 30 units are in the accompanying table. Complete parts a and b below. 750 815 505 705 870 910 615 375 890 690 530 620 955 865 845 985 825 930 675 600 545 770 860 950 415 585 800 810 555 970 a. What is the range of possible sampling error if a random sample of size n=6 is selected from the​ population? The possible sampling error ranges from ___to ____. b. What is the range of possible sampling error if a random sample of size n=10 is​ selected? The possible sampling error ranges from nothing to nothing. ​(Round to two decimal places as needed. Use ascending​ order.) Compare your answers to parts a and b and explain why the difference exists.

Answer 1

Following is the ordered data set:

	X
	375
	415
	505
	530
	545
	555
	585
	600
	615
	620
	675
	690
	705
	750
	770
	800
	810
	815
	825
	845
	860
	865
	870
	890
	910
	930
	950
	955
	970
	985
Total	22215

The population mean is:

(a)

The first six units and there total is:

	X
	375
	415
	505
	530
	545
	555
Total	2925

The mean of first six units is:

The sampling error for first six units is: 487.5 - 740.5 = -253

-------------

The last six units and there total is:

	X
	910
	930
	950
	955
	970
	985
Total	5700

The mean of last six units is:

The sampling error for last six units is: 950 - 740.5 = 209.5

So the possible sampling error ranges from -253 to 209.5.

(b)

The first 10 units and there total is:

	X
	375
	415
	505
	530
	545
	555
	585
	600
	615
	620
Total	5345

The mean of first 10 units is:

The sampling error for first six units is: 534.5 - 740.5 = -206

-------------

The last 10 units and there total is:

	X
	860
	865
	870
	890
	910
	930
	950
	955
	970
	985
Total	9185

The mean of last 10 units is:

The sampling error for last six units is: 918.5 - 740.5 = 178

So the possible sampling error ranges from -206 to 178.

As the sample size increases, range of sampling error decreases.