**Your class in Ancient Ugaritic Religion is poorly taught and the students have decided to complain to the dean. They decide to choose 4 of their number at random to carry the complaint. The class list appears below. Choose an SRS of 4 using the table of random digits beginning at line 145.**01 Anderson 02 Gutierrez 03 Patnaik 04 Aspin 05 Green 06 Pirelli 07 Bennett 08 Harter 09 Rao 10 Bock 11 Henderson 12 Rider 13 Breiman 14 Hughes 15 Robertson 16 Cochran 17 Johnson 18 Rodriguez 19 Dixon 20 Kim 21 Siegel 22 Edwards 23 Landis 24 Tompkins 25 Fuller 26 Laskowsky 27 Vandegraff 28 Grant 29 Olds 30 Williams Line 145: 19|

~~68~~|~~7 1~~|26|~~33~~|~~57~~|~~85~~|~~7 9~~|~~58~~|06 | 09|93|1 0|21|50

Choose persons: 19, 26, 06, and 09

These persons are: Dixon, Laskowsky, Pirelli, and Rao.*(Your answers my vary depending on how you numbered the names.)***A food processor has 50 large lots of canned mushrooms ready for shipment, each labeled with one of the lot numbers below. An SRS of 5 lots must be chosen for inspection. Use Table A to do this, beginning at line 139.**01 A1109 11 A2056 21 A2219 31 A2381 41 B0001 02 A1123 12 A2083 22 A2336 32 A2382 42 B0012 03 A1186 13 A2084 23 A2337 33 A2383 43 B0046 04 A1197 14 A2100 24 A2338 34 A2384 44 B1195 05 A1198 15 A2108 25 A2339 35 A2385 45 B1196 06 A2016 16 A2113 26 A2340 36 A2390 46 B1197 07 A2017 17 A2119 27 A2351 37 A2396 47 B1198 08 A2020 18 A2124 28 A2352 38 A2410 48 B1199 09 A2029 19 A2125 29 A2367 39 A2411 49 B1200 10 A2032 20 A2130 30 A2372 40 A2500 50 B1201 Line 139:

~~55~~|~~58~~|~~8 9~~|~~94~~|04 |~~70~~|~~70~~|~~8 4~~|10|~~98~~| 43|~~56~~|3 5|~~69~~|34

Choose lots: 04, 10, 43, 35, and 34

These lots are: A1197, A2032, B0046, A2385, and A2384*(Your answers my vary depending on how you numbered the lots.)***Which of the following statements are true of the table of random digits, and which are false?****There are exactly four 0s in each row of 40 digits.**False, such regularity holds only in the long run.

**Each pair of digits has chance 1/100 of being 00.**True.

**The digits 000 can never appear as a group because this pattern is not random.**False, 000 has chance 1 in 1000 to form any three consecutive digits, so it will occasionally occur (see Line 102 of Table A for an example).

**Below is a picture depicting a population of 80 circles. (They might represent fish in a pond or tumors removed in surgery.) Do a sampling experiment as follows:***(Your answers my vary depending on how you numbered the circles and which line you used.)***Label the circles 00, 01, . . ., 79 in any order, and use Table A to draw an SRS of size 4.**Line 110: 38|44|

~~8 4~~|~~87~~|~~89~~| 18|33|8 2|46|97

Circles chosen: 38, 44, 18, and 33

Diameters chosen: 0.625, 0.75, 0.75, and 0.875**Measure the diameter of each circle in your sample. (All of the circles have diameters that are multiples of 1/8 inch; in decimal form, the possible diameters are 1/8 - 0.125, 1/4 = 0.25, 3/8 = 0.375, 1/2 = 0.5, 5/8 = 0.625 3/4 - 0.75, and 7/8 = 0.875. Record your results in decimal form.) Then use a calculator to compute the mean diameter of the four circles in your sample. the mean of the diameters d1, d2, d3, and d4 is:****the ordinary average.**The average from the above sample is:

**Now repeat steps (a) and (b) three more times (four times in all), using a different part of Table A each time. Was any circle chosen more than once in your four SRSs? How different were the mean diameters for the four samples?**Line 118: 73|19|0 3|25|33

Circles chosen: 73, 19, 03, 25

Diameters chosen: 0.125, 0.125, 0.75, and 0.25

Mean diameter: 0.3125 inchesLine 126:

~~96~~|~~92~~|7 1|~~99~~|31 | 36|08|9 7|41|92

Circles chosen: 71, 31, 36, and 08

Diameters chosen: 0.75, 0.75, 0.125, and 0.875

Mean diameter: 0.625 inchesLine 143:

~~88~~|56|5 4|26|28

Circles chosen: 56, 54, 26, and 28

Diameters chosen: 0.5, 0.5, 0.25, and 0.875

Mean diameter: 0.53125 inchesNo circle was chosen more than once (although that is possible). The diameters ranged from 0.3125 inches to 0.75 inches.

**Now draw an SRS of size 16 from this population using a part of Table A not yet used in this exercise. Measure the diameters of the 16 circles in your sample and find the mean (average) diameter.**Line 106: 68|41|7 3|50|13 | 15|52|

~~9 7~~|27|65 |~~85~~|08|~~9 5~~|70|67 |~~50~~|21|1 4|74|~~87~~

Line 107:~~82~~|~~73~~|~~9 5~~|78|90

Circles chosen: 68, 41, 73, 50, 13, 15, 52, 27, 65, 08, 70, 67, 21, 14,74, and 78

Diameters chosen: 0.125, 0.25, 0.125, 0.25, 0.5, 0.625, 0.375, 0.5, 0.375, 0.875, 0.125, 0.125, 0.625, 0.5, 0.5, and 0.375

Mean diameter: 0.390625 inches

**Note:**There are 10 of each sized circle except for those with a diameter of 0.5 inches . . . there are 20 of these. Therefore, the population mean is 0.5 inches.

Please direct all questions regarding STAT-110 to your instructor or to the director of STAT-110, Dr. Todd Ogden at
*ogden@stat.sc.edu*.

Mail comments regarding this presentation to W. Scott Street, IV at *street@stat.sc.edu*.

© 1996 by W. Scott Street, IV