This presentation doesn't cover statistical topics from scratch.It's just a simple note summarize to ease statistical concepts for those who are already science associated students.

1. Statistics strategies flow
chart
VOLUME 1 - SAMPLE/POPULATION MANIPULATION.
EDITED BY: MOHAMMED ALI ISMAIL

2. Two ways to express data sets
 Proportions.
To say that (just examples) 40% of children like football, 60% of females read
poetry.
12% of air company flights are late… etc.
 Data parameters.
To say that (just examples) the mean of studying hours of a specific technical
course is 120 hrs with standard deviation of 10 hrs. The distance that an athletic
runs a day is 5 Km mean with standard deviation 500 mt… etc.

3. Inducing samples characteristics from
known population values.
 Central limit theorem
When we use data parameters.
 Population – Sample proportion means
When we talk about proportions.

4. Inducing samples characteristics from
known population values.
 Central limit theorem (When we use data parameters)
If sample size is larger than 30, then:
 The mean of the sample is equal to the population mean. ( = μ)
 Samples means distributions are following NORMAL Distribution.
 The sample variance is related to population variance by (S =
𝝈
𝒏
)
Where n is the sample size,  is the sample mean, μ is the population mean, S is
the sample standard deviation, and  is the population standard deviation.

5. Inducing samples characteristics from
known population values.
Example:
A tire production line indicates that the average weight of produced tires is 98.6 Kg and standard deviation is 0.73
Kg. If 36 tires are randomly chosen as a sample; what’s the probability that sample mean is under 98.3 Kg?
Solution:
 Step 1 (Problem data): n = 36, n = 98.3 Kg ,  = μ = 98.6 Kg ,  = 0.73 Kg, S = /√𝑛 = 0.122 Kg
 Step 2 (Calculate Z data): = (n - )/S = -2.459
 Step 3 (Use Standard Normal Distribution table to get probability):

6. Inducing samples characteristics from
known population values.
 Population – Sample proportion means (When we talk about proportions)
Sample should pass NORMAL DISTRIBUTION verification:
n*p≥5 n*(1-p)≥5
Where n is the sample size, and p is the population proportion.
AND

7. Inducing samples characteristics from
known population values.
Example:
It’s known that Russian tourism in Hurgada is about 79%. If a sample of 100 tourists in Hurgada is chosen randomly;
what is the probability that Russians represent more than 68% of the sample?
Solution:
 Step 1 (Problem data): n=100, p=0.79, pn=0.68
 Step 2 (Test verification):
n*p = 100*0.79 = 79 ≥ 5
n*(1-p) = 100*0.21 = 21 ≥ 5
 Step 3 (Calculate Z data ): = (pn-p)/√(p(1−p)/n) = -2.7
 Step 4 (Use Standard Normal Distribution table to get probability):
OK
OK
AND Verification OK

8. Inducing population values from sample
characteristics.
Data parameters
Estimating population mean Estimating population
standard deviation
n>30 n<30
Use LoC/Zc
Use
t-Student
Use Chi-Square
Distribution
Estimating population proportion