National open university of nigeria introduction to econometrics I eco 355

 
= 2.1797. These values show that the probability of a chi-square value 
exceeding 17.5346 is 2.5
 
percent and that of 2.1797 is 97.5 percent. Therefore, the 
interval between these two values is the 95% confidence interval for 
.
Substituting the data of our example into (4.4.3), the students should verify that the 95% 
confidence interval for 5 2 is as follows: 
(4.4.4)
The interpretation of this interval is: 
If we establish 95% confidence limits on 
a2 
and 
if we maintain a priori that these limits will include true a 2 , we shall be right in the long 
run 95 percent of the time. 
4.0 
CONCLUSION 
Confidence intervals consist of a range of values (interval) that act as good estimates of 
the unknown population parameter; however, the interval computed from a particular 
sample does not necessarily include the true value of the parameter. When we say, "we 
are 99% confident that the true value of the parameter is in our confidence interval", we 
express that 99% of the hypothetically observed confidence intervals will hold the true 
value of the parameter. After any particular sample is taken, the population parameter is 
either in the interval, realized or not; it is not a matter of chance. The desired level of 
confidence is set by the researcher (not determined by data). If a corresponding 
hypothesis test is performed, the confidence level is the complement of respective level 
of significance, i.e. a 95% confidence interval reflects a significance level of 0.05. 

---

92 
 
5.0
 
. SUMMARY 
In this unit we have learnt a lot on Confidence intervals and confident interval are 
frequently misunderstood, and published studies have shown that even professional 
scientists often misinterpret them. A 95% confidence interval does not mean that for a 
given realized interval calculated from sample data there is a 95% probability the 
population parameter lies within the interval, nor that there is a 95% probability that the 
interval covers the population parameter.
Once an experiment is done and an interval 
calculated, this interval either covers the parameter value or it does not, it is no longer a 
matter of probability. The 95% probability relates to the reliability of the estimation 
procedure, not to a specific calculated interval.