With a sample you can calculate the mean or a proportion of a variable. This result can be seen as an estimate for the total population. Because you can never be 100% sure whether this result applies to the entire population, you can calculate the confidence interval.
What is the confidence needed for
It is almost never possible to have all elements of the population in a research. For instance, in a research among Dutch inhabitants about their opinion on healthcare, it is not realistic to send a questionnaire to the 12.000.000 inhabitants of 18 years or older. Or in a research about working hours of the employees in ICT-companies in England it is hardly possible to collect data from every employee in every company. So researchers define the population, take a sample, wait a while for the response and then start to analyse the data from the respondents.
The results may give a fair impression, but do they reflect the opinion of all employees in the ICT-companies? Even if the response is representative of the population, it is not certain whether the results of the respondents reflect the opinion of the population. Nevertheless, it is the best guess and it is very likely it will hold. But can you be sure for hundred percent? No way, never!
What can be said about that? Well, don't be so vain to say you're right, because your research can not be wrong. A modest statement is something like this: "Based on the response, the calculated average is 45, but most likely the average for the population will be somewhere between 42 and 48." The numbers 42 and 48 are the minimum and maximum values of the confidence interval.
How to compute the confidence interval
A confidence interval can be computed for a mean or for a percentage. The formula for the mean is this one:
and for a percentage this formula has to be used:
Based on your response the mean, standard deviation or the p-value can be replaced by the numbers of the results. The only thing that is arbitrary is the number for the reliability (a/2). It is common to take the 90% reliability score, because then the confidence interval is smaller. Sometimes a reliability score of 95% is used, but this increases the confidence interval. With a 99% reliability, the confidence interval can be so wide that any reasonable value is acceptable. For example: ‘the average age of the inhabitants is 45 with a minimum of 10 and a maximum of 80’.