Question

Listed below are the rental agencies in the Automobile Rental section in the phone directory. Also noted is whether the rental agency is local (L), national (N), and whether the agency rents pickup trucks (T). Note that an agency could provide more than one service. Some of the agencies are to be randomly selected and asked various questions regarding the service they provide.

00	ADA Auto Rentals	L		10	General Motors Rental System	L,N,T
01	Alamo Rent a Car	L,N		11	Hertz Rent a Car	L,N,T
02	Avis Rent a Car	L,N		12	Lee’s Sales and Service	L,T
03	Bill’s Towing	L,T		13	National Car Rental	L,N
04	Budget Car and Truck Rental	L,N,T		14	Quality Imports	L
05	Charlie’s Dodge	L,T		15	Rent a Wreck	L,T
06	EZ Rent a Car	L		16	Sears Car and Truck Rental	L,N,T
07	Enterprise	L,N		17	Thrifty Car Rental	L,N
08	Ford Rental System	L,N,T		18	Toyota Car Rental	L,N,T
09	Guardian Car Rentals	L,N		19	Wagoner Motor Sales	L,T

Use Appendix B.6 – Table of Random Numbers for the following problems:

      a.   Randomly select a sample of five rental agencies. Start with row two and column two. The number is 90935. Use the first two numbers starting with 90.

      b.   Randomly select a second sample of five rental agencies starting at the bottom left corner of the table. The number is 11084. Use the far right two digits starting with 84.

      c.   Randomly select a sample of six that consists of every third rental agency starting with 02.

      d.   Select a sample of four rental agencies so that one of each type is included. Start at the top of column three. The number is 75997. Use the left two digits starting with 75.

      e.   Randomly select a sample of five rental agencies that rent trucks. Start at the bottom of the third column of the table. The number is 78957. Use the far right two digits starting with 57.

      f.    Randomly select a sample of two rental agencies that rent locally and nationally, but do not rent trucks. Start at the bottom of the fourth column of the table. The number is 77353. Use the second and third set of digits starting with 73.

      g.   Use the table of random numbers to select your sample of five rental agencies. Specify in your answer where you started in the random number table and how you chose that starting point

Answer 1

Given data

The rental agency is local (L), national (N), and  the agency rents pickup trucks (T)

00	ADA Auto Rentals	L		10	General Motors Rental System	L,N,T
01	Alamo Rent a Car	L,N		11	Hertz Rent a Car	L,N,T
02	Avis Rent a Car	L,N		12	Lee’s Sales and Service	L,T
03	Bill’s Towing	L,T		13	National Car Rental	L,N
04	Budget Car and Truck Rental	L,N,T		14	Quality Imports	L
05	Charlie’s Dodge	L,T		15	Rent a Wreck	L,T
06	EZ Rent a Car	L		16	Sears Car and Truck Rental	L,N,T
07	Enterprise	L,N		17	Thrifty Car Rental	L,N
08	Ford Rental System	L,N,T		18	Toyota Car Rental	L,N,T
09	Guardian Car Rentals	L,N		19	Wagoner Motor Sales	L,T

a)

a random sample of five rental agencies 00, 04, 14, 15, 19, found by: Start with row two and column two. The number is 90935. Use the first two numbers starting with 90. The column is repeated below with the selected numbers in bold and italics.

            90, 78, 97, 00, 19, 04, 14, 57, 81, 26, 25, 67, 22, 19 skip, 72, 90, 76, 36, 87, 97, 47, 25, 15

            We select rental agency number 00, 04, 14, 15, 19.     

b)

The sample is agency numbers 02, 03, 04, 06, 15, found by: Starting at the bottom left corner of the table, the number is 11084. Use the far right two digits starting with 84. The column is repeated below with the selected numbers in bold and italics.

            84, 43, 48, 86, 15, 91, 06, 96, 50, 35, 24, 34, 43, 38, 69, 68, 83, 99, 61, 02, 84, 69, 78, 26, 55, 90, 03, 44, 82, 37, 65, 43, 50, 74, 64, 92, 71, 81, 94, 73, 04

          We select rental agency number 02, 03, 04, 06, 15.

c)

Every third rental agency starting with 02 is: 02, 05, 08, 11, 14, 17.

d)

The sample is agency numbers 02(LN), 06(L), 11(LNT), and 12(LT), found by: In order to select a sample of four rental agencies so that one of each type of agency is included, we had to skip a selection when we had already selected an agency for that category. The different agencies are L, LN, LT and LNT. Starting at the top of column three, the number is 75997. Use the left two digits starting with 75. The column is repeated below with the selected numbers in bold and italics and underline.

            75, 31, 06(L), 37, 93, 22, 92, 50, 91, 53, 28, 89, 93, 90, 12(LT), 37, 43, 92, 01(L) Skip, 33, 11(LNT), 40, 43, 37, 06(L) Skip, 40, 90, 38, 51, 28, 21, 89, 95, 39, 76, 95, 36, 25, 49, 47, 46, 29, 24, 93, 52, 77, 62, 04(LNT) Skip, 46, 78, 95, 59, 02(LN),             

            We select rental agency number 02, 06, 11 and 12.

e)

The sample is agency numbers 03LT, 04LNT, 11LNT, 16LNT, 18LNT, found by: In order to select a sample of five rental agencies that rent trucks, we will need to skip agencies that only rent local (L) and those agencies that rent only local (L) and National (N). Starting at the bottom of the third column, the number is 78957. Use the far right two digits starting with 57. The column is repeated below with the selected numbers in bold italics and underlined:

            57, 98, 28, 92, 03(LT), 68, 86, 11(LNT), 90, 84, 41, 55, 00 Skip, 99, 45, 54, 58, 28, 26, 27, 98, 35, 90, 48, 59, 35, 38, 70, 98, 38, 04(LNT), 72, 25, 39, 22, 95, 26, 04(LNT) Skip, 78, 72, 09(LN) Skip, 85, 73, 60, 97, 51, 97, 35, 84, 97, 59, 16(LNT), 66, 73, 32, 24, 24, 03(LT) Skip, 11(LNT) 38, 84, 91, 35, 03(LT) Skip, 24, 77, 33, 29, 11(LNT) Skip, 33, 18(LNT).    We select rental agency number 03LT, 04LNT, 11LNT, 16LNT, and 18LNT,

f)   

      The sample is agency numbers 01LN, 09LN, 17 LN, found by: In order to select a sample of two rental agencies that rent locally and nationally, but do not rent trucks, we will need to skip all agencies that rent trucks (T). Starting at the bottom of the fourth column of the table, the number is 77353. Use the second and third set of digits starting with 73. The column is repeated below with the selected numbers in bold, italics, and underlined.

            73, 45, 69, 66, 09(LN), 94, 01(LN), 73, 37, 17(LN).   We select agencies 01LN, 09LN, 17 LN.

g)

Using the table of random numbers to select a sample of five rental agencies will result in numerous samples depending on the starting point in the table.

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