 Hello and welcome to the session. In this session we will discuss population and sample proportions, confidence interval and margin of error. Here we can use statistics to make influences about population from a sample of population. Now let us define population and sample proportions. First of all let us see population proportion is ratio of members of population with a particular characteristic to the total members of population and it is denoted by small letter P it is mean of population and now let us see sample proportion it is ratio of members of sample of population with a particular characteristic to the total members of sample. Now if x is the number of individuals with a particular characteristic in the sample and n is the total number individuals in sample then sample proportion is given like which is equal to x upon n Here we have a sample proportion mean of sample. Now suppose we know the sample mean and we want to estimate population mean or proportion. Now see when we have sample is greater than 30 when we estimate population proportion from sample proportion then value of population proportion will not be a particular number because there is a difference between the actual true value and the estimated value it means there will be a small error in this calculation is called margin error. Now to cover up this error we will find a range in which the true value of the population proportion will lie thus it will be an interval. So we find an interval which may include value of population mean or population proportion and these intervals are called intervals and these confidence intervals. Now whenever we have sample of size n greater than 30 the sample distribution is always normal distribution so we have normal curve for the distribution normal curve and we know the sample mean now we want to estimate population mean mu which is same as population proportion which is denoted by smaller to p mu may be equal to may not be equal to x bar and to cover up this difference we will consider 95% of area under normal curve. Now here this yellow shaded portion represents 95% of area under this normal curve we assume that the true value of the population will lie in this interval that is from x bar minus 2 sigma to x bar plus 2 sigma thus we take 95% confidence intervals we take 99% or 90% confidence intervals but generally we take it to be 95% Now formula for calculating confidence interval is sample mean margin of error but more precisely the following formula is used to find a range of population proportion p for 95% confidence intervals and that is p hat minus 2 into square root of p hat times 1 minus p hat the whole protocol n is less than p is less than p hat plus 2 into square root of into 1 minus p hat the whole whole upon p represents population proportion, p hat represents sample proportion. Then we have discussed population proportion, confidence interval and margin of error. And this completes our session. Hope you all have enjoyed the session.