Type of Type of Number Physician Practice Number Physician Practice
1
00 R. E. Scherbarth, M.D.
2
S 20 Gregory Yost, M.D.
3
P 01 Crystal R. Goveia, M.D.
4
P 21 J. Christian Zona, M.D.
5
P 02 Mark D. Hillard, M.D.
6
P 22 Larry Johnson, M.D.
7
P 03 Jeanine S. Huttner, M.D.
8
P 23 Sanford Kimmel, M.D.
9
P 04 Francis Aona, M.D.
10
P 24 Harry Mayhew, M.D.
11
S 05 Janet Arrowsmith, M.D.
12
P 25 Leroy Rodgers, M.D.
13
S 06 David DeFrance, M.D.
14
S 26 Thomas Tafelski, M.D.
15
S 07 Judith Furlong, M.D.
16
S 27 Mark Zilkoski, M.D.
17
G 08 Leslie Jackson, M.D.
18
G 28 Ken Bertka, M.D.
19
G 09 Paul Langenkamp, M.D.
20
S 29 Mark DeMichiei, M.D.
21
G 10 Philip Lepkowski, M.D.
22
S 30 John Eggert, M.D.
23
P 11 Wendy Martin, M.D.
24
S 31 Jeanne Fiorito, M.D.
25
P 12 Denny Mauricio, M.D.
26
P 32 Michael Fitzpatrick, M.D.
27
P 13 Hasmukh Parmar, M.D.
28
P 33 Charles Holt, D.O.
29
P 14 Ricardo Pena, M.D.
30
P 34 Richard Koby, M.D.
31
P 15 David Reames, M.D .
32
P 35 John Meier, M.D.
33
P 16 Ronald Reynolds, M.D.
34
G 36 Douglas Smucker, M.D.
35
S 17 Mark Steinmetz, M.D.
36
G 37 David Weldy, M.D.
37
P 18 Geza Torok, M.D.
38
S 38 Cheryl Zaborowski, M.D.
39
P 19 Mark Young, M.D. P
a. The random numbers obtained from Appendix B.6 (above) are: 31, 94, 43, 36, 03, 24,
17, and What is sampling error?
Sampling error
Two types of errors are possible in a statistical study. They are sampling errors and
non sampling errors. The term sampling error refers to those errors which occur due
to the fact the study is conducted using a sample only. If the entire population is
investigated, then there will be no sampling error. The sampling error will be more for
small samples and will be small for large samples.
Non sampling errors are errors in measurements, collection, classification and
tabulation.
Could the value of the sampling error be zero?
The sampling error will be zero if and only if the sample is the same as the population.
If it were zero, what would this mean?
If the sampling error is zero it means we have studied the population itself. If the sampling
error is zero and at the same time the complete population is not investigated, then the
possibilities are (1) all the items in the population are the same or (2) a very rare event has
happened, the probability of which is almost zero.
New Question here relating to Appendix B.6 info = Chapter 8, Exercise 22 List the reasons
for sampling. Give an example of each reason for sampling
The sampling method has the following merits over the complete enumeration survey:
1.
2.
3.
4.
5.
6.
Less time consuming: since the sample is only a part of the population considerable
time and labour are saved when a sample survey is carried out.
Less cost: The total financial burden of a sample survey is generally less than a
complete census.
More reliable results: Although the sampling technique involves, certain inaccuracies
owing to sampling errors, the result obtained is generally more than that obtained for
a complete survey. First, it is always possible to determine the extent of sampling
errors. Secondly, more effective precautions can be taken in a sample survey to ensure
that the information is accurate and complete. Thirdly, it is possible to avail the
services of experts and to impart thorough training to the investigators in a sample
survey which further reduces the possibility of errors.
More detailed information: Since the sampling technique saves time and money, it is
possible to collect more detailed information in a sample survey.
Sampling method is the only method that can be used in certain cases: If the
population is infinite, nonexistent or hypothetical, then the only method available for
collecting data is sampling method. If the process of taking information destroys the
unit, then also we can adopt only the sampling method.
The sampling method can be used to test the accuracy of the information obtained in a
census survey.
New Question Chapter 3, Exercise 5 Compute the mean of the following sample values:
16.25, 12.91, 14.58
Mean = Σx/n = (16.25 + 12.91 + 14.58) /3 =43.74/3 = 14.58
New Question As a condition of employment, fashion industries applicants must pass a drug
test. of the last 220 applicants 14 failed the test. Develop a 99% confidence interval for the
proprotion of applicants that fail the test.
Sample size = n = 220
Sample proportion = P = 14/220 = 0.0636
𝑃(1−𝑃)
99% confidence interval for population = P ±𝑧0.01/2√
= 0.0636 ± 2.58√
𝑛
0.0636(1 − 0.0636)
= 0.0636 ± 0.0165 = 0.0471,
220
0.0801
The 99% confidence interval is (0.0471, 0.0801)
Would it be reasonable to conclude that more than 10% of the applicants are now failing the
test?
Let the population proportion be denoted by 𝜋.
Null hypothesis H0: 𝜋 = 𝜋0 = 0.10
Alternative hypothesis: 𝜋 > 0.10
𝑧=
𝑃 − 𝜋0
√𝜋0 (1 − 𝜋0 )
𝑛
=
0.0636 − 0.10
√0.10(1 − 0.10)
220
= −1.7979
The critical region for this test is z> 1.65 at 5% level and 𝑧 > 2.33 at 1% level. The z value
does not fall in the critical region. The null hypothesis cannot be rejected.
It is not reasonable conclude that more than 10% of the applicants are falling failing the test.
In addition to the testing of applicants, fashion industries randomly tests its employees
throughout the year. Last year in the 400 random tests conducted, 14 employees failed the
test. Would it be reasonable to conclude that less than 5% of the employees are not able to
pass the random test
n = 400
P = 14/400 = 0.035
H0: 𝜋 = 0.05
H1: 𝜋 < 0.05
𝑧=
0.035−0.05
0.05(1−0.05)
400
= −1.3765
√
The critical region at 5% level is 𝑍 < −1.65
The critical region at 1% level is Z<-2.33
The z is not significant. We cannot reject the null hypothesis
We cannot that less than 5% of employees are not able to pass the test.