STAT-110: Homework (Sec. 1.2)

STAT-110

Instructor: Scott Street

Homework Solutions (Section 1.2)


  1. 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.
    01Anderson
    02Gutierrez
    03Patnaik
    04Aspin
    05Green
    06Pirelli
    07Bennett
    08Harter
    09Rao
    10Bock
    11Henderson
    12Rider
    13Breiman
    14Hughes
    15Robertson
    16Cochran
    17Johnson
    18Rodriguez
    19Dixon
    20Kim
    21Siegel
    22Edwards
    23Landis
    24Tompkins
    25Fuller
    26Laskowsky
    27Vandegraff
    28Grant
    29Olds
    30Williams

    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.)

  2. 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.
    01A1109
    11A2056
    21A2219
    31A2381
    41B0001
    02A1123
    12A2083
    22A2336
    32A2382
    42B0012
    03A1186
    13A2084
    23A2337
    33A2383
    43B0046
    04A1197
    14A2100
    24A2338
    34A2384
    44B1195
    05A1198
    15A2108
    25A2339
    35A2385
    45B1196
    06A2016
    16A2113
    26A2340
    36A2390
    46B1197
    07A2017
    17A2119
    27A2351
    37A2396
    47B1198
    08A2020
    18A2124
    28A2352
    38A2410
    48B1199
    09A2029
    19A2125
    29A2367
    39A2411
    49B1200
    10A2032
    20A2130
    30A2372
    40A2500
    50B1201

    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.)

  3. Which of the following statements are true of the table of random digits, and which are false?

    1. There are exactly four 0s in each row of 40 digits.

      False, such regularity holds only in the long run.

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

      True.

    3. 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).

  4. 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.)

    1. 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

    2. 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:

    3. 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 inches

      Line 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 inches

      Line 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 inches

      No circle was chosen more than once (although that is possible). The diameters ranged from 0.3125 inches to 0.75 inches.

    4. 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.


T.O.C.BackNext


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.


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© 1996 by W. Scott Street, IV