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Sampling Techniques and Statistical Inference Three Marks Questions

12th Standard

    Reg.No. :
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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
    10 x 3 = 30
  1. Using the Kendall-Babington Smith - Random number table, Draw 5 random samples.

    23 15 75 48 59 01 83 72 59 93 76 24 97 08 86 95 23 03 67 44
    05 54 55 50 43 10 53 74 35 08 90 61 18 37 44 10 96 22 13 43
    14 87 16 03 50 32 40 43 62 23 50 05 10 03 22 11 54 36 08 34
    38 97 67 49 51 94 05 17 58 53 78 80 59 01 94 32 42 87 16 95
    97 31 26 17 18 99 75 53 08 70 94 25 12 58 41 54 88 21 05 13
  2. Using the following Tippett’s random number table,

    2952 6641 3992 9792 7969 5911 3170 5624
    4167 9524 1545 1396 7203 5356 1300 2693
    2670 7483 3408 2762 3563 1089 6913 7991
    0560 5246 1112 6107 6008 8125 4233 8776
    2754 9143 1405 9025 7002 6111 8816 6446

    Draw a sample of 15 houses from Cauvery Street which has 83 houses in total.

  3. Using the following random number table,

    Tippet’s random number table
    2952 6641 3992 9792 7969 5911 3170 5624
    4167 9524 1545 1396 7203 5356 1300 2693
    2670 7483 3408 2762 3563 1089 6913 7991
    0560 5246 1112 6107 6008 8125 4233 8776
    2754 9143 1405 9025 7002 6111 8816 6446

    Draw a sample of 10 children with their height from the population of 8,585 children as classified here under.

    Height (cm) 105 107 109 111 113 115 117 119 121 123 125
    Number of children 2 4 14 41 83 169 394 669 990 1223 1329
    Height(cm) 127 129 131 133 135 137 139 141 143 145  
    No. of children 1230 1063 646 392 202 79 32 16 5 2  
  4. Using the following random number table (Kendall-Babington Smith)

    23 15 75 48 59 01 83 72 59 93 76 24 97 08 86 95 23 03 67 44
    05 54 55 50 43 10 53 74 35 08 90 61 18 37 44 10 96 22 13 43
    14 87 16 03 50 32 40 43 62 23 50 05 10 03 22 11 54 36 08 34
    38 97 67 49 51 94 05 17 58 53 78 80 59 01 94 32 42 87 16 95
    97 31 26 17 18 99 75 53 08 70 94 25 12 58 41 54 88 21 05 13

    Draw a random sample of 10 four- figure numbers starting from 1550 to 8000.

  5. From the following data, select 68 random samples from the population of heterogeneous group with size of 500 through stratified random sampling, considering the following categories as strata.
    Category 1: Lower income class - 39%
    Category 2: Middle income class - 38%
    Category 3: Upper income class - 23%

  6. A server channel monitored for an hour was found to have an estimated mean of 20 transactions transmitted per minute. The variance is known to be 4. Find the standard error.

  7. Find the sample size for the given standard deviation 10 and the standard error with respect of sample mean is 3.

  8. A die is thrown 9000 times and a throw of 3 or 4 is observed 3240 times. Find the standard error of the proportion for an unbiased die. .

  9. The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard deviation is 6?

  10. A sample of 100 students is chosen from a large group of students. The average height of these students is 162 cm and standard deviation (S.D) is 8 cm. Obtain the standard error for the average height of large group of students of 160 cm?

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