To obtain information about a population parameter, such as the value of population mean µ or population proportion ?, a random sample of objects from the population is usually created. Then, the sample statistic found from the values of the sample observations is used for predictions about population parameter.

Generally, the process of estimating a population parameter by a single number derived from the sample is called point estimation.

1. An unknown population parameter is to be estimated.
2. A sample including n independent observations is selected randomly from the population and a particular function of the sample observations is used as an estimate of the parameter.
3. The sample observations are obtained from the independent random variables X1, X2, ... Xn. Thus, the statistic to be calculated is also a random variable. Therefore, the probability distribution of the statistic is called its sampling distribution.

Generally, the probability distribution of a sample statistic is called sampling distribution of the statistic. A sample statistic is a random variable before the sample observation’s selection. However, after the sampling, a statistic is simply a number.

Using the point estimation approach, we can safely say that the value of the population weight is equal to the 12.50 kilogram.

The sampling distribution of the sample mean is the probability distribution of all possible sample means that can be created from a population with a fixed sample size of n.

Central limit theorem is one of the most important theorems in statistics. If you take independent samples one by one from a population with a known arithmetic mean and standard deviation and calculate the means of these samples, central limit theorem states that the shape of the distribution of the sample means will be approximately Normal distribution. Central Limit Theorem also indicates that without the regard of the shape of a population parameter’s distribution (symmetric, asymmetric, left skewed or right skewed), the sampling distribution of the sample mean approximates to the normal distribution as the sample size increases.

While it is known that the value of the point estimate of a population parameter gets closer to real value of population parameter as sample size increases, we would like to measure how close the point estimate really is to the actual value. For this purpose, interval estimation is used. An interval estimation of a population parameter, demonstrated by ? in general, includes two limits or boundaries.

There are two important situations in the calculation of confidence interval for a population mean. The first case is that we use sample data to estimate the unknown value of population mean µ with the value of sample mean found from a random sample of size n, and also the population standard deviation ? is known beforehand. The second case is that we use sample data to estimate the unknown value of population µ with the value of sample mean found from a random sample of size n, and also the population standard deviation ? is not known. In the second case, instead of the population standard deviation ?, the sample standard deviation s is used as the substitute.

It would be '15.5'.

We call this 'Point Estimation'. 

The population proportion estimate of female students in this class is 41/57. 

The point estimate of the population arithmetic mean of the same variable is 65.

The point estimate of population proportion for broken products is '0.02'.

The upper limit of the confidence interval is 55. 

The sample arithmetic mean that was used in this confidence interval problem is 155.

This estimation procedure is called Interval Estimation.

The value of the standard error that is be used in the confidence interval calculations is 4.