Assignment on statistical inference #Statistics #mathematics #science

1. Assignment on Statistical inference
Course title: Biostatistics
Minhaj University Lahore

2. Statistical Inference:
Statistical
Inference
Topic:
Statistical Inference:
Topic:

3. Statistical inference:
 The process of drawing inference about population on the basis
of sample data is called statistical inference.
 It is also called inferential statistics.
Example:
When we go to the market to buy a product, then we test it and
after that we decide whether we should purchase it or not.

4. Statistical inference:
For accuracy:
 Sample must be drawn randomly.
 Every segment of the population adequately represented in sample.
Population
Parameter
Data
Statistic
Sample
Inference

5. Statistical inference based on:
1. Surveys.
2. Experiments.
3. Publications.
Statistical inference may based on data collected in surveys or experiments.
For example; when we want to obtain information from people, we may use
 Interviews.
 Online.
 Opinion polls.
In such surveys, however minimize any nonresponse bias.

6. Nonresponse bias:
Some people say yes in the survey, some say no. But some will simply not
respond to the survey. SO, it must be minimize during survey.

7. Experiments:
In this method data will come from experiments.

8. Publications:
Data may come from published sources. Such as
 Making statistical inference in such cases may be complex and difficult.
 We must also be careful to note any missing data or incomplete observation.

9. Statistical inference:
Estimation Testing of hypothesis
Decision making procedure
about hypothesis.
Point
estimation
Interval
estimation
Confidence interval
( mean, variance, proportion)

10. Types of statistical
inference:
There are two types of statistical inference.
1. Estimation.
2. Testing of hypothesis.

11.  Estimation:
A process in which we obtain the values of unknown population
parameters with the help of sample data.
Here we must know about:
Population: Population is the totality .
Sample: Sample is the small part of the population.

12. Estimate:
An estimate is the numerical value of an estimator.
Estimator:
It is a rule formula or function that tells how to calculate an
estimate

13.  Types of estimation:
 Point estimation.
 Interval mutation.
Point Estimation:
When an estimate for unknown population parameter is
expressed by a single value. It is called Point estimation.

14. Interval estimation:
When an estimate is expressed by the range of values is called the interval estimate and the
process is called interval estimation.
Example of point estimation and interval estimation:
 If we wish to estimate temperature of a place and we state the temperature is 29 degree
centigrade then it is called point mutation.
 and if we state the temperature is in between 20 degree centigrade and 30 degree
centigrade. So it is called interval estimation.

15. Example of Estimation:
 When we find estimate for population mean (𝜇) 𝑤𝑒 𝑢𝑠𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑚𝑒𝑎𝑛 𝑥 𝑏𝑎𝑟.
× = ∑ × / 𝒙
 It is a rule, formula or function called an estimator.
Suppose x bar is equal to 10. 10 is numeric value of estimator and is
called an estimate. And our answer is in single numeric form it is also
called point estimator.
The whole process is called estimation.
-

16. Why Statistical inference?
 Why we take statistical inference?
 Why not just look at our data and interpret them?
Because:
If no. of observations are small, you can interpret
it easily but if there is a larger population and you
want to interpret it, firstly you take randomly
sample from it then make statistical inference of it
and then by finding statistical analysis you can
find out population parameter. After that you
become able to draw conclusion on that big
population.

17. Acknowledgement:
 Firstly, we all likely to thank almighty Allah who provides us knowledge, energy
and skills to get opportunities and increase our knowledge.
 Secondly, I thank to my instructor Sir Haider who guides me and give me a chance
to study this interesting and informative topic.

18. References:
 Box GEP,Tiao GC (1973) Bayesian inference in statistical analysis.Addison-
WesleyGoogle Scholar.
 Cox DR (2006) Principles of statistical inference, Cambridge University Press,
CambridgezbMATHGoogle Scholar.
 Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis, 2nd edn.
Chapman and Hall/CRC Press, Boca Raton, FLzbMATHGoogle Scholar.
 Agresti,A. and Coull, B.A. (1998). Approximate is better than "exact" for interval
estimation of binomial proportions",The American Statistician, 52(2), 119-126.
 Brown, L. D. Cai,T.T. and DasGupta, A. (2001). Interval estimation for a binomial
proportion", Statistical Science, 16(2), 101-133