This lecture was given as a part of the Introduction to Epidemiology & Community Medicine Course given for third-year medical students.

1. Chapter 3
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2. Dr Ahmed Hussein 2
confidence interval

3.  Definition of statistical inference :
Statistical inference is defined as a selection random
sample from the population to study the properties of this
population.
 Statistical inference topics :
Statistical inference includes two statistical topics:
Statistical estimation.
1) Point Estimation.
2) Confidence interval estimation.
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4. First: Statistical inference about population mean µ
The population mean µ:
Where N is population size
 Estimation of population mean
1) Point estimate:
Sample mean:
is the point estimate for population mean µ, n is
sample size.
N
X
N
i
i
 1

n
X
X

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5. 2) Interval Estimates:
Many researchers prefer estimating range which includes
population mean µ with probability (1-α) called
confidence level, and this range named confidence
interval. And this done by using equation.
Application(1):
Assume that we select random sample of 8 experimental
units, and measure the production of tomato by kg/unit,
the following table show the values.
  
Errorstandardis
n
S
ESand
TtabulatedisTWhere
ESTEstimationError
EstimationErrorX
n
n





.
:
.
)1,2/1(
)1,2/1(


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6. 1) Find the point estimate of population mean of
production.
2) Calculate 95% confidence interval for population
mean and explain it.
Solution Application(1)
Sample mean is point estimate of population mean (µ).
Calculate 95% confidence interval for population mean
unit 1 2 3 4 5 6 7 8
X(production) 97 87 102 113 112 117 78 98
5.100
8
804


n
x
X
EstimationErrorX 
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7. X X-X (X-X)2
97 -3.5 12.25
87 -13.5 182.25
102 1.5 2.25
113 12.5 156.25
112 11.5 132.25
117 16.5 272.25
78 -22.5 506.25
98 -2.5 6.25
0 1270
Standard deviation(S) =
(𝑋−𝑋)2
𝑛−1
=
1270
7
= 13.47
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8. S.E = S/ n = 13.47 / 8 = 4.76
T at (n-1 , 0.05) = 2.365
Error Estimation = (T) . (S.E) = (2.365) (4.76) = 11.26
Then Confidence Interval : 100.5 - 11.26 , 100.5 + 11.26
Then Confidence Interval : 89.24 , 111.76
I am at 95% confidence that population mean of
production lies between 89.24 and 111.76 kg/unit.
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9. Dr Ahmed Hussein 9

10. Application(2):
Assume that we select random sample of 5
experimental units, and measure the production
of tomato by kg/unit, the following table show
the values.
Calculate 99% confidence interval for population
mean and explain it.
7 9 10 12 12
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11. Solution Application(2):-
X = 50/5 = 10
s = 18/4 = 2.12
X X-X (X-X)2
7 -3 9
9 -1 1
10 0 0
12 2 4
12 2 4
0 18
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12. S.E = S/ n = 2.12 / 5 = 0.95
T at (n-1 , 0.01) = 4.604
Error Estimation = (T) . (S.E) = (4.604) (0.95) = 4.3738
Then Confidence Interval : 10 - 4.3738 , 10 + 4.3738
Then Confidence Interval : 5.6262 , 14.3738
I am at 99% confidence that population mean of
production lies between 5.6262 and 14.3738 kg/unit.
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13. H.w
Assume that we select random sample of 7
experimental units, and measure the production
of tomato by kg/unit, the following table show
the values.
Calculate 95% confidence interval for population
mean and explain it.
10 8 7 5 6 9 4
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