Assignmnet: Simple Random Sampling With Replacement

1
Assignmnet Simple Random Sampling With
Replacement

• Some Solutions

2
Question 2 SRSWR

• a. What is the formula to estimate the sample
  variance

3
Question 2. (SRSWR)

• 2c. (a54p10.sas). Do any samples occur where the
  same patient was selected on each of the
  selections?
• Which ones?
• What is the chance (probability) that this will
  happen?
• Is the number of times that the same subject was
  selected each time equal to what you would
  expect?
• Why or why not.

4
2c. (a54p10.sas).

• Do any samples occur where the same patient was
  selected on each of the selections? (Note sid1,
  sid2, etc are the subject IDs)
• PROC PRINT DATAd NOOBS SPLIT""
• VAR sample sid1-sid3
• TITLE2 "Table 2. List of nsamp Simple Random
  Samples "
• RUN

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2c. (a54p10.sas).

• Table 2. List of 40 Simple Random Samples
• 1st 2nd 3rd
• ID ID ID
• sample Sel. Sel. Sel.
• 1 5 6 6
• 2 3 3 6
• 3 2 2 3
• 4 6 3 1
• 5 3 3 3 Subject 3
  selected each time
• 6 1 1 4
• 7 6 5 5
• 8 4 6 4
• 9 4 3 6
• 10 1 6 5
• 11 5 4 4
• 12 1 6 5
• 13 4 2 3

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2c. (a54p10.sas).

• Do any samples occur where the same patient was
  selected on each of the selections? (Add these
  statements to tabulate distinct samples)
• DATA d1
• SET d
• snum100sid110sid2sid3
• RUN
• PROC PRINT DATAd1 NOOBS SPLIT""
• VAR sample snum sid1-sid3
• TITLE2 "Table 2a. List of nsamp Simple Random
  Samples "
• RUN
• PROC FREQ DATAd1
• TABLES snum
• TITLE2 "Table 2b. Subjects in nsamp Samples
  with replacement"
• RUN

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2c. (a54p10.sas).

• Table 2b. Subjects in 40 Samples with
  replacement
• The FREQ Procedure
• Cumulative
  Cumulative
• snum Frequency Percent Frequency
  Percent
• ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
  ƒƒƒƒƒƒƒ
• 114 1 2.50 1
  2.50
• 121 1 2.50 2
  5.00
• 143 1 2.50 3
  7.50
• 165 3 7.50 6
  15.00
• 166 1 2.50 7
  17.50
• 213 1 2.50 8
  20.00
• 215 1 2.50 9
  22.50
• 223 2 5.00 11
  27.50
• 231 1 2.50 12
  30.00
• 232 1 2.50 13
  32.50
• 233 1 2.50 14
  35.00
• 236 1 2.50 15
  37.50

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Assignment SRSWR

• 2c. (a54p10.sas). What is the chance
  (probability) that the same patient was selected
  on each of the selections?

of samples
of samples with same selection 111, 222, 333,
444, 555, 666
9
Assignment SRSWR

• 2c. (a54p10.sas). Is the number of times that
  the same subject was selected each time equal to
  what you would expect?

of samples expected
No- we observed 3, and only expected 1.11
samples. This may be because we only took 40
samples.
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Question 3 SRSWR

• a. If we count samples as different if either
  the subjects included are different or if the
  order of selection of subjects is different, how
  many different possible sample could we select?

Note that N6, n3
N
N
N
Sample ______ _______
______ Position 1 Position 2
Position 3
This counts the samples as different for all
subjects selected in all orders.
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3b. How many times would you expect that each
sample would occur if 4320 samples were selected?
Question 3 SRSWR
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Question 3 SRSWR

• g. Suppose that three different subjects are
  selected. In how many different orders can 3
  different subjects be selected (this is the
  number of permutations).

ID1, ID2, ID3
n-2
n-1
n
Sample ______ _______
______ Position 1 Position 2
Position 3
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When Sampling Without Replacement3a. If we
count samples as different if either the subjects
included are different, or if the order of
selection of subjects is different, how many
different possible samples could we select?

• N6, n3

N-2
N-1
N
Sample ______ _______
______ Position 1 Position 2
Position 3
14
When Sampling Without Replacement3b. How many
times would you expect that each sample would
occur if 4320 samples were selected?
15
When Sampling Without Replacement3b. In how
many different orders can the same three subjects
be selected? (This is the number of
permutations.)