MathematicsHands on Determination of Confidence Interval of a population Mean - Term Paper Example

STATISTICS EXERCISES By of the of the School Objective The main objective of this paper is to determine the confidence interval and the population mean of the Cholesterol level in men. We use a sample data; the main difference between a population and sample has to do with how observations are assigned to the data set.MeanThe mean, or μ, is the average of a set of measurements. It can be viewed as the expected outcome E(x) of an event x, such that if the measurement is performed multiple times, the average value would be the most common outcome.

The sample mean is the average value of a sample, which is a finite series of measurements, and is an estimate of the population mean. The sample mean, denoted , is calculated with the formulaUsing the cholesterol data we got the mean to be;VarianceThe variance and standard deviation are related indicators of the spread of data within a population or sample.  The population variance is calculated using the population meanUsing the cholesterol data we got the mean to be;Standard deviationStandard deviation, , measures the amount of variation or dispersion from the average.

A low standard deviation indicates that the data points tend to be very close to the mean (also called expected value); a high standard deviation indicates that the data points are spread out over a large range of values.Sampling usedSimple random samplingThis refers to a method of probability sampling in which a sample of n elements is randomly chosen without replacement from a population of N elements.Confidence intervalA confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

The width of the confidence interval gives us some idea about how uncertain we are about the unknown parameter (see precision). A very wide interval may indicate that more data should be collected before anything very definite can be said about the parameter.For the cholesterol data the confidence interval (CI) is given as;ReferencesMoore, David S. and George P. McCabe (2006), Introduction to the Practice of Statistics, fifth edition, Freeman, p. 219.Walker, Helen (1931). Studies in the History of the Statistical Method.

Baltimore, MD: Williams & Wilkins Co. pp. 24–25.