Milena Velba En Le Autobus

Range of confidence for the mean μ of a normal population with known standard deviation σ

Assuming a population that follows a distribution Z ~ N (0.1) is sufficient to find the critical point zα / 2 to take an interval containing the population mean with probability c.

p (-zα / 2 <>

If we take the general case:

           

                                                                    

bastará con hacer unas sencillas operaciones para llegar a que el intervalo de confianza para la media μ de una población normal con desviación típica conocida σ es:

confidence interval for the mean μ of a population with known standard deviation σ

For populations that are not normal, or simply do not know if they are or not, we need the size the sample is sufficiently large (n> 30) to apply the Central Limit Theorem to obtain the confidence interval for the mean μ of a population with known standard deviation σ is:

confidence interval for the mean μ of a population with unknown standard deviation

When unknown population standard deviation estimator is used as the standard deviation of the sample with the confidence interval for the mean μ of a population with unknown standard deviation is:

Determination of sample size

A typical problem is to determine the minimum sample size for confidence interval for the mean with a given confidence level has an error bound equal to a known quantity .

To calculate the minimum sample size is sufficient to raise equality:

where:

If the value you get is whole take is the smallest integer greater than the value obtained.

These problems do not need to know the sample mean. If you know the sample mean can be determined by the confidence interval.